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THE  CONCEPT  OF  NATURE 


CAMBRIDGE  UNIVERSITY  PRESS 

C.  F.  CLAY,  Manager 

LONDON  :  FETTER  LANE,  E.C.  4 


NEW  YORK  :  THE  MACMILLAN  CO. 

BOMBAY      ") 

CALCUTTA  [-MACMILLAN  AND  CO.,  Ltd. 

MADRAS      J 

TORONTO    :   THE    MACMILLAN    CO.   OF 

CANADA,  Ltd. 
TOKYO  :  MARUZEN-KABUSHIKI-KAISHA 

ALL  RIGHTS  RESERVED 


THE  CONCEPT  OF  NATURE 

TARNER  LECTURES  DELIVERED  IN  TRINITY  COLLEGE 
NOVEMBER  1919 


BY 


A.  N.  WHITEHEAD,  Sc.D.,  F.R.S. 

FELLOW  OF  TRINITY  COLLEGE,  CAMBRIDGE,  AND 

PROFESSOR  OF  APPLIED  MATHEMATICS  IN 

THE  IMPERIAL  COLLEGE  OF  SCIENCE 

AND  TECHNOLOGY 


CAMBRIDGE 

AT  THE  UNIVERSITY  PRESS 

1920 


PREFACE 


The  contents  of  this  book  were  originally  delivered  at 
Trinity  College  in  the  autumn  of  19 19  as  the  inaugural 
course  of  Tarner  lectures.  The  Tarner  lectureship  is 
an  occasional  office  founded  by  the  liberality  of 
Mr  Edward  Tarner.  The  duty  of  each  of  the  successive 
holders  of  the  post  will  be  to  deliver  a  course  on  *  the 
Philosophy  of  the  Sciences  and  the  Relations  or  Want 
of  Relations  between  the  different  Departments  of 
Knowledge.'  The  present  book  embodies  the  endeavour 
of  the  first  lecturer  of  the  series  to  fulfil  his  task. 

The  chapters  retain  their  original  lecture  form  and 
remain  as  delivered  with  the  exception  of  minor 
changes  designed  to  remove  obscurities  of  expression. 
The  lecture  form  has  the  advantage  of  suggesting  an 
audience  with  a  definite  mental  background  which  it  is 
the  purpose  of  the  lecture  to  modify  in  a  specific  way. 
In  the  presentation  of  a  novel  outlook  with  wide  rami- 
fications a  single  line  of  communications  from  premises 
to  conclusions  is  not  sufficient  for  intelligibility.  Your 
audience  will  construe  whatever  you  say  into  conformity 
with  their  pre-existing  outlook.  For  this  reason  the  first 
two  chapters  and  the  last  two  chapters  are  essential 
for  intelligibility  though  they  hardly  add  to  the  formal 
completeness  of  the  exposition.  Their  function  is  to 
prevent  the  reader  from  bolting  up  side  tracks  in  pursuit 
of  misunderstandings.  The  same  reason  dictates  my 
avoidance   of  the   existing  technical   terminology   of 


VI  PREFACE 

philosophy.  The  modern  natural  philosophy  is  shot 
through  and  through  with  the  fallacy  of  bifurcation 
which  is  discussed  in  the  second  chapter  of  this  work. 
Accordingly  all  its  technical  terms  in  some  subtle  way 
presuppose  a  misunderstanding  of  my  thesis.  It  is 
perhaps  as  well  to  state  expHcitly  that  if  the  reader 
indulges  in  the  facile  vice  of  bifurcation  not  a  word  of 
what  I  have  here  written  will  be  intelligible. 

The  last  two  chapters  do  not  properly  belong  to  the 
special  course.  Chapter  VIII  is  a  lecture  delivered  in 
the  spring  of  1920  before  the  Chemical  Society  of 
the  students  of  the  Imperial  College  of  Science  and 
Technology.  It  has  been  appended  here  as  conveniently 
summing  up  and  applying  the  doctrine  of  the  book 
for  an  audience  with  one  definite  type  of  outlook. 

This  volume  on  *the  Concept  of  Nature'  forms  a 
companion  book  to  my  previous  work  An  Enquiry  con- 
cerning the  Principles  of  Natural  Knowledge,  Either 
book  can  be  read  independently,  but  they  supplement 
each  other.  In  part  the  present  book  supplies  points 
of  view  which  were  omitted  from  its  predecessor;  in 
part  it  traverses  the  same  ground  with  an  alternative 
exposition.  For  one  thing,  mathematical  notation  has 
been  carefully  avoided,  and  the  results  of  mathematical 
deductions  are  assumed.  Some  of  the  explanations  have 
been  improved  and  others  have  been  set  in  a  new  light. 
On  the  other  hand  important  points  of  the  previous 
work  have  been  omitted  where  I  have  had  nothing  fresh 
to  say  about  them.  On  the  whole,  whereas  the  former 
work  based  itself  chiefly  on  ideas  directly  drawn  from 


PREFACE  vii 

mathematical  physics,  the  present  book  keeps  closer 
to  certain  fields  of  philosophy  and  physics  to  the  ex- 
clusion of  mathematics.  The  two  works  meet  in  their 
discussions  of  some  details  of  space  and  time. 

I  am  not  conscious  that  I  have  in  any  way  altered  my 
views.  Some  developments  have  been  made.  Those 
that  are  capable  of  a  non-mathematical  exposition  have 
been  incorporated  in  the  text.  The  mathematical  de- 
velopments are  alluded  to  in  the  last  two  chapters.  They 
concern  the  adaptation  of  the  principles  of  mathematical 
physics  to  the  form  of  the  relativity  principle  which  is 
here  maintained.  Einstein's  method  of  using  the  theory 
of  tensors  is  adopted,  but  the  application  is  worked 
out  on  different  lines  and  from  different  assumptions. 
Those  of  his  results  which  have  been  verified  by 
experience  are  obtained  also  by  my  methods.  The 
divergence  chiefly  arises  from  the  fact  that  I  do  not 
accept  his  theory  of  non-uniform  space  or  his  assump- 
tion as  to  the  peculiar  fundamental  character  of  light- 
signals.  I  would  not  however  be  misunderstood  to  be 
lacking  in  appreciation  of  the  value  of  his  recent  work 
on  general  relativity  which  has  the  high  merit  of  first 
disclosing  the  way  in  which  mathematical  physics 
should  proceed  in  the  light  of  the  principle  of  relativity. 
But  in  my  judgment  he  has  cramped  the  development 
of  his  brilliant  mathematical  method  in  the  narrow 
bounds  of  a  very  doubtful  philosophy. 

The  object  of  the  present  volume  and  of  its  pre- 
decessor is  to  lay  the  basis  of  a  natural  philosophy  which 
is  the  necessary  presupposition  of  a  reorganised  specu- 


viii  PREFACE 

lative  physics.  The  general  assimilation  of  space  and 
time  which  dominates  the  constructive  thought  can 
claim  the  independent  support  of  Minkowski  from  the 
side  of  science  and  also  of  succeeding  relativists,  while  on 
the  side  of  philosophers  it  was,  I  believe,  one  theme  of 
Prof.  Alexander's  GifFord  lectures  delivered  some  few 
years  ago  but  not  yet  published.  He  also  summarised 
his  conclusions  on  this  question  in  a  lecture  to  the 
AristoteUan  Society  in  the  July  of  191 8.  Since  the 
publication  of  An  Enquiry  concerning  the  Principles  of 
Natural  Knowledge  I  have  had  the  advantage  of  reading 
Mr  C.  D.  Broad's  Perception ^  Physics ^  and  Reality 
[Camb.  Univ.  Press,  1914].  This  valuable  book  has 
assisted  me  in  my  discussion  in  Chapter  II,  though  I 
am  unaware  as  to  how  far  Mr  Broad  would  assent  to 
any  of  my  arguments  as  there  stated. 

It  remains  for  me  to  thank  the  staff  of  the  University 
Press,  its  compositors,  its  proof-readers,  its  clerks,  and 
its  managing  officials,  not  only  for  the  technical  ex- 
cellence of  their  work,  but  for  the  way  they  have 
co-operated  so  as  to  secure  my  convenience. 

A.  N.  W. 


IMPERIAL  COLLEGE  OF  SCIENCE 
AND  TECHNOLOGY. 

Aprily  1920. 


CONTENTS 

CHAP.  PAGE 

I  NATURE  AND  THOUGHT      .         .         .         .         .  i 

II  THEORIES  OF  THE  BIFURCATION  OF  NATURE  .  26 

III  TIME 49 

IV  THE  METHOD  OF  EXTENSIVE  ABSTRACTION   .  74 

V  SPACE  AND  MOTION 99 

VI  CONGRUENCE 120 

VII  OBJECTS 143 

VIII  SUMMARY -^       .     164 

IX  THE  ULTIMATE  PHYSICAL  CONCEPTS        .         .185 

NOTE  :  On  the  Greek  Concept  of  a  Point  .  .  .197 
NOTE:  On  Significance  and  Infinite  Events  .  .197 
INDEX 199 


^ 


THE  CONCEPT  OF  NATURE 

CHAPTER  I 

NATURE  AND  THOUGHT 

The  subject-matter  of  the  Tarner  lectures  is  defined  by 
the  founder  to  be  '  the  Philosophy  of  the  Sciences  and 
the  Relations  or  Want  of  Relations  between  the  different 
Departments  of  Knowledge.'  It  is  fitting  at  the  first 
lecture  of  this  new  foundation  to  dwell  for  a  few  moments 
on  the  intentions  of  the  donor  as  expressed  in  this 
definition;  and  I  do  so  the  more  willingly  as  I  shall 
thereby  be  enabled  to  introduce  the  topics  to  which  the 
present  course  is  to  be  devoted. 

We  are  justified,  I  think,  in  taking  the  second  clause 
of  the  definition  as  in  part  explanatory  of  the  earlier 
clause.  What  is  the  philosophy  of  the  sciences?  It  is 
not  a  bad  answer  to  say  that  it  is  the  study  of  the  rela- 
tions between  the  different  departments  of  knowledge. 
Then  with  admirable  solicitude  for  the  freedom  of 
learning  there  is  inserted  in  the  definition  after  the 
word  *  relations'  the  phrase  *or  want  of  relations.'  A 
disproof  of  relations  between  sciences  would  in  itself 
constitute  a  philosophy  of  the  sciences.  But  we  could 
not  dispense  either  with  the  earlier  or  the  later  clause. 
It  is  not  every  relation  between  sciences  which  enters 
into  their  philosophy.  For  example  biology  and  physics 
are  connected  by  the  use  of  the  microscope.  Still,  I  may 
safely  assert  that  a  technical  description  of  the  uses  of 
the  microscope  in  biology  is  not  part  of  the  philosophy 
of  the  sciences.   Again,  you  cannot  abandon  the  later 


2  THE  CONCEPT  OF  NATURE  [ch. 

clause  of  the  definition;  namely  that  referring  to  the 
relations  between  the  sciences,  without  abandoning  the 
explicit  reference  to  an  ideal  in  the  absence  of  which 
philosophy  must  languish  from  lack  of  intrinsic  interest. 
That  ideal  is  the  attainment  of  some  unifying  concept 
which  will  set  in  assigned  relationships  within  itself  all 
that  there  is  for  knowledge,  for  feeling,  and  for  emotion. 
That  far  off  ideal  is  the  motive  power  of  philosophic 
research;  and  claims  allegiance  even  as  you  expel  it. 
The  philosophic  pluralist  is  a  strict  logician;  the 
Hegelian  thrives  on  contradictions  by  the  help  of  his 
absolute;  the  Mohammedan  divine  bows  before  the 
creative  will  of  Allah ;  and  the  pragmatist  will  swallow 
anything  so  long  as  it  *  works.' 

The  mention  of  these  vast  systems  and  of  the  age- 
long controversies  from  which  they  spring,  warns  us 
to  concentrate.  Our  task  is  the  simpler  one  of  the 
philosophy  of  the  sciences.  Now  a  science  has  already 
a  certain  unity  which  is  the  very  reason  why  that  body 
of  knowledge  has  been  instinctively  recognised  as 
forming  a  science.  The  philosophy  of  a  science  is  the 
endeavour  to  express  explicitly  those  unifying  charac- 
teristics which  pervade  that  complex  of  thoughts  and 
make  it  to  be  a  science.  The  philosophy  of  the  sciences 
— conceived  as  one  subject — is  the  endeavour  to  exhibit 
all  sciences  as  one  science,  or — in  case  of  defeat — ^the 
disproof  of  such  a  possibility. 

Again  I  will  make  a  further  simplification,  and  con- 
fine attention  to  the  natural  sciences,  that  is,  to  the 
sciences  whose  subject-matter  is  nature.  By  postulating 
a  common  subject-matter  for  this  group  of  sciences,  a 
unifying  philosophy  of  natural  science  has  been  thereby 
presupposed. 


I] 


NATURE  AND  THOUGHT 


What  do  we  mean  by  nature?  We  have  to  discuss 
the  philosophy  of  natural  science.  Natural  science  is 
the  science  of  nature.  But — ^What  is  nature.? 

Nature   is   that   which   we   observe   in   perception  1^ 
through  the  senses.    In  this  sense-perception  we  are/ 
aware  of  something  which  is  not  thought  and  which  is 
self-contained  for  thought.  This  property  of  being  self- 
contained  for  thought  lies  at  the  base  of  natural  science. 
It  means  that  nature  can  be  thought  of  as  a  closed 


system  whose  mutual  relations   do  not  require  the  jj 
expression  of  the  fact  that  tTiey^feTthoughtabout.  [ 

I'hus  in  a  sense  nature  is  independent  of  thought.  By  i 
this  statement  no  metaphysical  pronouncement  is  in-| 
tended.  What  I  mean  is  that  we  can  think  about  nature 
without  thinking  about  thought.    I  shall  say  that  then 
we  are  thinking  *  homogeneously '  about  nature. 

Of  course  it  is  possible  to  think  of  nature  in  conjunc- 
tion with  thought  about  the  fact  that  nature  is  thought 
about.  In  such  a  case  I  shall  say  that  we  are  thinking 
*  heterogeneously '  about  nature.  In  fact  during  the  last 
few  minutes  we  have  been  thinking  heterogeneously 
about  nature.  Natural  science  is  exclusively  concerned 
with  homogeneous  thoughts  about  nature. 

But  sense-perception  has  in  it  an  element  which  is 
not  thought.  It  is  a  difficult  psychological  question 
whether  sense-perception  involves  thought;  and  if  it 
does  involve  thought,  what  is  the  kind  of  thought  which 
it  necessarily  involves.  Note  that  it  has  been  stated' 
above  that  sense-perception  is  an  awareness  of  some-  \ 
thing  which  is  not  thought.  Namely,  nature  is  not/ 
thought.  But  this  is  a  different  question,  namely  that 
the  fact  of  sense-perception  jias^  factor  which  is_ not 
thought.   I  catl^his  factor  *  sense-awareness.'  Accord- 


I — 2 


4  THE  CONCEPT  OF  NATURE  [ch. 

ingly  the  doctrine  that  natural  science  is  exclusively 
concerned  with  homogeneous  thoughts  about  nature 
does  not  immediately  carry  with  it  the  conclusion  that 
natural  science  is  not  concerned  with  sense-awareness. 
However,  I  do  assert  this  further  statement ;  namely, 
that  though  natural  science  is  concerned  with  nature 
which  is  the  terminus  of  sense-perception,  it  is  not  con- 
cerned with  the  sense-awareness  itself. 

I  repeat  the  main  line  of  this  argument,  and  expand 
it  in  certain  directions. 

Thought  about  nature  is  different  from  the  sense- 
perception  of  nature.  Hence  the  fact  of  sense-perception 
has  an  ingredient  or  factor  which  is  not  thought.  I  call 
this  ingredient  sense-awareness.  It  is  indifferent  to  my 
argument  whether   sense-perception   has   or  has   not 
thought  as  another  ingredient.  If  sense-perception  does 
\    \     not  involve  thought,  then  sense-awareness  and  sense- 
fT^  |,  perception  are  identical.   But  the  something  perceived 
f\Jrlf^^  perceived  as  an  entity  which  is  the  terminus  of  the 
'v^pT  sense-awareness,    something    which    for    thought    is 
rjf  I    beyond  the  fact  of  that  sense-awareness.    Also  the 
^  something  perceived  certainly  does  not  contain  other 

sense-awarenesses  which  are  different  from  the  sense- 
T         awareness  which  is  an  ingredient  in  that  perception. 
p'^Af^l  Accordingly  nature  as  disclosed  in  sense-perception  is 
«r^^    self-contained  as  against  sense-awareness,  in  addition 
J^       to  being  self-contained  as  against  thought.   I  will  also 
'    '  *    express  this  self-containedness  of  nature  by  saying  that 
nature  is  closed  to  mind. 

This  closure  of  nature  does  not  carry  with  it  any 
metaphysical  doctrine  of  the  disjunction  of  nature  and 
mind.  It  means  that  in  sense-perception  nature  is 
disclosed  as  a  complex  of  entities  whose  mutual  relations 


// 


I]  NATURE  AND  THOUGHT  5 

are  expressible  in  thought  without  reference  to  mind, I 
that  is,  without  reference  either  to  sense-awareness  or 
to  thought.  Furthermore,  I  do  not  wish  to  be  under- 
stood as  implying  that  sense-awareness  and  thought  are 
the  only  activities  which  are  to  be  ascribed  to  mind. 
Also  I  am  not  denying  that  there  are  relations  of  natural 
entities  to  mind  or  minds  other  than  being  the  termini 
of  the  sense-awarenesses  of  minds.  Accordingly  I  will 
extend  the  meaning  of  the  terms  *  homogeneous 
thoughts'  and  *  heterogeneous  thoughts'  which  have 
already  been  introduced.  We  are  thinking  *  homogene- 
ously' about  nature  when  we  are  thinking  about  it 
without  thinking  about  thought  or  about  sense-aware- 
ness, and  we  are  thinking  *  heterogeneously '  about 
nature  when  we  are  thinking  about  it  in  conjunction 
with  thinking  either  about  thought  or  about  sense- 
awareness  or  about  both. 

I  also  take  the  homogeneity  of  thought  about  nature 
as  excluding  any  reference  to  moral  or  aesthetic  values 
whose  apprehension  is  vivid  in  proportion  to  self- 
conscious  activity.  The  values^of  nature  are  perhaps  the 
key  to  the  metaphysical  svntV>esis  of  pyistpnrp^  But  such 
a  synthesis  is  exactly  what  I  am  not  attempting.  I  am 
concerned  exclusively  with  the  generalisations  of  widest 
scope  which  can  be  effected  respecting  that  which  is 
known  to  us  as  the  direct  deliverance  of  sense-awareness. 

I  have  said  that  nature  is  disclosed  in  sense-percep- 
tion as  a  complex  of  entities.  It  is  worth  considering 
what  we  mean  by  an  entity  in  this  connexion.  *  Entity' 
is  simply  the  Latin  equivalent  for  *  thing '  unless  some 
arbitrary  distinction  is  drawn  between  the  words  for 
technical  purposes.  All  thought  has  to  be  about  things. 
We  can  gain  some  idea  of  this  necessity  of  things  for 


6  THE  CONCEPT  OF  NATURE  [ch. 

thought  by  examination  of  the  structure  of  a  proposi- 
tion. 

Let  us  suppose  that  a  proposition  is  being  communi- 
cated by  an  expositor  to  a  recipient.  Such  a  proposition 
is  composed  of  phrases ;  some  of  these  phrases  may  be 
demonstrative  and  others  may  be  descriptive. 

By  a  demonstrative  phrase  I  mean  a  phrase  which 
makes  the  recipient  aware  of  an  entity  in  a  way  which 
is  independent  of  the  particular  demonstrative  phrase. 
You  will  understand  that  I  am  here  using  *  demonstra- 
tion' in  the  non-logical  sense,  namely  in  the  sense  in 
which  a  lecturer  demonstrates  by  the  aid  of  a  frog  and 
a  microscope  the  circulation  of  the  blood  for  an  ele- 
mentary class  of  medical  students.  I  will  call  such 
demonstration  '  speculative '  demonstration,  remember- 
ing Hamlet's  use  of  the  word  '  speculation'  when  he 

says, 

There  is  no  speculation  in  those  eyes. 

Thus  a  demonstrative  phrase  demonstrates  an  entity 
speculatively.  It  may  happen  that  the  expositor  has 
meant  some  other  entity — ^namely,  the  phrase  demon- 
strates to  him  an  entity  which  is  diverse  from  the  entity 
which  it  demonstrates  to  the  recipient.  In  that  case 
there  is  confusion ;  for  there  are  two  diverse  propositions, 
namely  the  proposition  for  the  expositor  and  the  pro- 
position for  the  recipient.  I  put  this  possibility  aside 
as  irrelevant  for  our  discussion,  though  in  practice  it 
may  be  difficult  for  two  persons  to  concur  in  the  con- 
sideration of  exactly  the  same  proposition,  or  even  for 
one  person  to  have  determined  exactly  the  proposition 
which  he  is  considering. 

Again  the  demonstrative  phrase  may  fail  to  demon- 
strate any  entity.   In  that  case  there  is  no  proposition 


I]  NATURE  AND  THOUGHT  7 

for  the  recipient.  I  think  that  we  may  assume  (perhaps 
rashly)  that  the  expositor  knows  what  he  means. 

A  demonstrative  phrase  is  a  gesture.  It  is  not  itself 
a  constituent  of  the  proposition,  but  the  entity  which  it 
demonstrates  is  such  a  constituent.  You  may  quarrel 
with  a  demonstrative  phrase  as  in  some  way  obnoxious 
to  you;  but  if  it  demonstrates  the  right  entity,  the 
proposition  is  unaffected  though  your  taste  may  be 
offended.  This  suggestiveness  of  the  phraseology  is  part 
of  the  literary  quality  of  the  sentence  which  conveys 
the  proposition.  This  is  because  a  sentence  directly 
conveys  one  proposition,  while  in  its  phraseology  it 
suggests  a  penumbra  of  other  propositions  charged  with 
emotional  value.  We  are  now  talking  of  the  one  pro- 
position directly  conveyed  in  any  phraseology. 

This  doctrine  is  obscured  by  the  fact  that  in  most 
cases  what  is  in  form  a  mere  part  of  the  demonstrative 
gesture  is  in  fact  a  part  of  the  proposition  which  it  is 
desired  directly  to  convey.  In  such  a  case  we  will  call 
the  phraseology  of  the  proposition  elliptical.  In  ordinary- 
intercourse  the  phraseology  of  nearly  all  propositions 
is  elliptical. 

Let  us  take  some  examples.  Suppose  that  the  ex- 
positor is  in  London,  say  in  Regent's  Park  and  in 
Bedford  College,  the  great  women's  college  which  is 
situated  in  that  park.  He  is  speaking  in  the  college  hall 
and  he  says, 

'This  college  building  is  commodious.' 

The  phrase  '  this  college  building '  is  a  demonstrative 
phrase.   Now  suppose  the  recipient  answers, 

*  This  is  not  a  college  building,  it  is  the  lion-house  in 
the  Zoo.' 

Then,  provided  that  the  expositor's  original  proposi- 


8  THE  CONCEPT  OF  NATURE  [ch. 

tion  has  not  been  couched  in  elHptical  phraseology,  the 
expositor  sticks  to  his  original  proposition  when  he 
replies, 

'Anyhow,  it  is  commodious.' 

Note  that  the  recipient's  answer  accepts  the  specula- 
tive demonstration  of  the  phrase '  This  college  building.' 
He  does  not  say,  *  What  do  you  mean? '  He  accepts  the 
phrase  as  demonstrating  an  entity,  but  declares  that 
same  entity  to  be  the  lion-house  in  the  Zoo.  In  his 
reply,  the  expositor  in  his  turn  recognises  the  success 
of  his  original  gesture  as  a  speculative  demonstration, 
and  waives  the  question  of  the  suitability  of  its  mode  of 
suggestiveness  with  an  *  anyhow.'  But  he  is  now  in  a 
position  to  repeat  the  original  proposition  with  the  aid 
of  a  demonstrative  gesture  robbed  of  any  suggestiveness, 
suitable  or  unsuitable,  by  saying, 

'It  is  commodious.' 

The  'it^  of  this  final  statement  presupposes  that 
thought  has  seized  on  the  entity  as  a  bare  objective  for 
consideration. 

^  We  confine  ourselves  to  entities  disclosed  in  sense- 
awareness.  The  entity  is  so  disclosed  as  a  relatum  in  the 
complex  which  is  nature.  It  dawns  on  an  observer 
because  of  its  relations ;  but  it  is  an  objective  for  thought 
in  its  own  bare  individuality.  Thought  cannot  proceed 
otherwise ;  namely,  it  cannot  proceed  without  the  ideal 
bare  *it'  which  is  speculatively  demonstrated.  This 
setting  up  of  the  entity  as  a  bare  objective  does  not 
ascribe  to  it  an  existence  apart  from  the  complex  in 
which  it  has  been  found  by  sense-perception.  The  'it' 
\for  thought  is  essentially  a  relatum  for  sense-awareness. 

The  chances  are  that  the  dialogue  as  to  the  college 
building  takes  another  form.    Whatever  the  expositor 


I]  NATURE  AND  THOUGHT  9 

originally  meant,  he  almost  certainly  now  takes  his 
former  statement  as  couched  in  elliptical  phraseology, 
and  assumes  that  he  was  meaning, 

*  This  is  a  college  building  and  is  commodious.' 
Here  the  demonstrative  phrase  or  the  gesture,  which 

demonstrates  the  *it'  which  is  commodious,  has  now 
been  reduced  to  *  this ' ;  and  the  attenuated  phrase,  under 
the  circumstances  in  which  it  is  uttered,  is  sufficient  for 
the  purpose  of  correct  demonstration.  This  brings  out 
the  point  that  the  verbal  form  is  never  the  whole  phrase- 
ology of  the  proposition ;  this  phraseology  also  includes 
the  general  circumstances  of  its  production.  Thus  the  aim 
of  a  demonstrative  phrase  is  to  exhibit  a  definite  *  it '  as  a 
bare  objective  for  thought ;  but  the  modus  operandi  of 
a  demonstrative  phrase  is  to  produce  an  awareness  of 
the  entity  as  a  particular  relatum  in  an  auxiliary  complex, 
chosen  merely  for  the  sake  of  the  speculative  demon- 
stration and  irrelevant  to  the  proposition.  For  example, 
in  the  above  dialogue,  colleges  and  buildings,  as  related 
to  the  *it'  speculatively  demonstrated  by  the  phrase 
*this  college  building,'  set  that  *it'  in  an  auxiliary 
complex  which  is  irrelevant  to  the  proposition 

*  It  is  commodious.' 

Of  course  in  language  every  phrase  is  invariably 
highly  elliptical.  Accordingly  the  sentence 

*  This  college  building  is  commodious ' 
means  probably 

'This  college  building  is  commodious  as  a  college 
building.' 

But  it  will  be  found  that  in  the  above  discussion 
we  can  replace  *  commodious'  by  *  commodious  as  a 
college  building'  without  altering  our  conclusion; 
though  we  can  guess  that  the  recipient,  who  thought 


10  THE  CONCEPT  OF  NATURE  [ch. 

he  was  in  the  Hon-house  of  the  Zoo,  would  be  less  likely 
to  assent  to 

*  Anyhow,  it  is  commodious  as  a  college  building.' 
A  more  obvious  instance  of  elliptical  phraseology 

arises  if  the  expositor  should  address  the  recipient  with 
the  remark, 

'That  criminal  is  your  friend.' 
The  recipient  might  answer, 
*He  is  my  friend  and  you  are  insulting.' 
Here  the  recipient  assumes  that  the  phrase  'That 
criminal'  is  elliptical  and  not  merely  demonstrative.  Jn 
fact,  pure  demonstration  is  impossible  thoudi  it  is  the 
ideal  of^thought .  This  practical  impossibility  of  pure 
demonstration  is  a  difficulty  which  arises  in  the  com- 
munication of  thought  and  in  the  retention  of  thought. 
Namely,  a  proposition  about  a  particular  factor  in  nature 
can  neither  be  expressed  to  others  nor  retained  for 
repeated  consideration  without  the  aid  of  auxiliary  com- 
plexes which  are  irrelevant  to  it. 

I  now  pass  to  descriptive  phrases.  The  expositor  says, 

*  A  college  in  Regent's  Park  is  commodious.' 

The  recipient  knows  Regent's  Park  well.  The  phrase 
*A  college  in  Regent's  Park'  is  descriptive  for  him.  If 
its  phraseology  is  not  elliptical,  which  in  ordinary  life 
it  certainly  will  be  in  some  way  or  other,  this  proposition 
simply  means, 

'There  is  an  entity  which  is  a  college  building  in 
Regent's  Park  and  is  commodious.' 

If  the  recipient  rejoins, 

'  The  lion-house  in  the  Zoo  is  the  only  commodious 
building  in  Regent's  Park,' 

he  now  contradicts  the  expositor,  on  the  assumption 
that  a  lion-house  in  a  Zoo  is  not  a  college  building. 


I]  NATURE  AND  THOUGHT  ii 

Thus  whereas  in  the  first  dialogue  the  recipient 
merely  quarrelled  with  the  expositor  without  con- 
tradicting him,  in  this  dialogue  he  contradicts  him.  Thus 
a  descriptive  phrase  is  part  of  the  proposition  which  it 
helps  to  express,  whereas  a  demonstrative  phrase  is  not 
part  of 'the  proposition  which  it  helps  to  express. 

Again  the  expositor  might  be  standing  in  Green  Park 
— ^where  there  are  no  college  buildings — and  say, 

*This  college  building  is  commodious.' 

Probably  no  proposition  will  be  received  by  the 
recipient  because  the  demonstrative  phrase, 

*This  college  building' 
has  failed  to  demonstrate  owing  to  the  absence  of  the 
background  of  sense-awareness  which  it  presupposes. 

But  if  the  expositor  had  said, 

'A  college  building  in  Green  Park  is  commodious,' 
the  recipient  would  have  received  a  proposition,  but  a 
false  one. 

Language  is  usually  ambiguous  and  it  is  rash  to  make 
general  assertions  as  to  its  meanings.  But  phrases  which 
commence  with '  this '  or  *  that '  are  usually  demonstrative, 
whereas  phrases  which  commence  with  *the'  or  *a' 
are  often  descriptive.  In  studying  the  theory  of  pro- 
positiond  expression  it  is  important  to  remember  the 
wide  difference  between  the  analogous  modest  words 
*this'  and  'that'  on  the  one  hand  and  *a'  and  *the' 
on  the  other  hand.  The  sentence 

*The  college  building  in  Regent's  Park  is  com- 
modious ' 

means,  according  to  the  analysis  first  made  by  Bertrand 
Russell,  the  proposition, 

*  There  is  an  entity  which  (i)  is  a  college  building  in 
Regent's  Park  and  (ii)  is  commodious  and  (iii)  is  such 


12  THE  CONCEPT  OF  NATURE  [CH. 

that  any  college  building  in  Regent's  Park  is  identical 
with  it.' 

The  descriptive  character  of  the  phrase  *  The  college 
building  in  Regent's  Park'  is  thus  evident.  Also  the 
proposition  is  denied  by  the  denial  of  any  one  of  its 
three  component  clauses  or  by  the  denial  of  any 
combination  of  the  component  clauses.  If  we  had 
substituted  *  Green  Park'  for  *  Regent's  Park'  a  false 
proposition  would  have  resulted.  Also  the  erection  of  a 
second  college  in  Regent's  Park  would  make  the  pro- 
position false,  though  in  ordinary  life  common  sense 
would  politely  treat  it  as  merely  ambiguous. 

*  The  Iliad '  for  a  classical  scholar  is  usually  a  demon- 
strative phrase ;  for  it  demonstrates  to  him  a  well-known 
poem.  But  for  the  majority  of  mankind  the  phrase  is 
descriptive,  namely,  it  is  synonymous  with  '  The  poem 
named  "the  Iliad".' 

Names  may  be  either  demonstrative  or  descriptive 
phrases.  For  example  'Homer'  is  for  us  a  descriptive 
phrase,  namely,  the  word  with  some  slight  difference 
in  suggestiveness  means  *The  man  who  wrote  the 
Iliad.' 

This  discussion  illustrates  that  thought  places  before 
itself  bare  objectives,  entities  as  we  call  them,  which 
the  thinking  clothes  by  expressing  their  mutual  rela- 
tions. Sense-awareness  discloses  fact  with  factors  which 
are  the  entities  for  thought.  The  s.eparate^distinction  of 
an  entity  in  thought  is  not  a  metaphysical  assertioa>_blit 


'  a  methodof  procedure  necessaryfor  the  finite  expression 

of  mdividual  propositions.    Apart  from  entities  there 

'could  be  no  finite  truths ;  they  are  the  means  by  which 

the  infinitude  of  irrelevance  is  kept  out  of  thought. 

\To  sum  up:  the  termini  for  thought  are  entities > 


I]  NATURE  AND  THOUGHT  13 

primarily  with__bare  individuality,  secondarily  with 
properties  and  relations  ascribed  to  them  jn_the  pro- 
cedure of  thought ;  the  termini  for  sense-awareness  are 
factors  in  the  fact  of  nature,.4:u:imarily  relata  andjonly 
secondarily  discriminated  as  distinct  individualities. 

No  characteristic  of  nature  which  is  immediately 
posited  for  knowledge  by  sense-awareness  can  be 
explained.  It  is  impenetrable  by  thought,  in  the  sense 
that  its  peculiar  essential  character  which  enters  into 
experience  by  sense-awareness  is  for  thought  merely  the 
guardian  of  its  individuality  as  a  bare  entity.  Thus  for 
thought  *red'  is  merely  a  definite  entity,  though  for 
awareness  *  red '  has  the  content  of  its  individuality.  The 
transition  from  the  *red'  of  awareness  to  the  *red'  of 
thought  is  accompanied  by  a  definite  loss  of  content, 
namely  by  the  transition  from  the  factor  *red'  to  the/ 
entity  *red.'  This  loss  in  the  transition  to  thought  is] 
compensated  by  the  fact  that  thought  is  communicable/ 
whereas  sense-awareness  is  incommunicable. 

Thus  there  are  three  components  in  our  knowledge  of 
nature,  namely,  fact,  factors,  and  entities.  Fact  is  the 
undifferentiated  terminus  of  sense-awareness;  factors 
are  termini  of  sense-awareness,  differentiated  as  elements 
of  fact ;  entities  are  factors  in  their  function  as  the  ter- 
mini of  tfiougEt.  The  entities  thus  spoken  of  are  natural 
entities.  Thought  is  wider  than  nature,  so  that  there  are 
entities  for  thought  which  are  not  natural  entities. 

When  we  speak  of  nature  as  a  complex  of  related 
entities,  the  *  complex'  is  fact  as  an  entity  for  thought, 
to  whose  bare  individuality  is  ascribed  the  property  of 
embracing  in  its  complexity  the  natural  entities.  It  is 
our  business  to  analyse  this  conception  and  in  the  course 
of  the  analysis  space  and  time  should  appear.  Evidently 


14  THE  CONCEPT  OF  NATURE  [ch. 

Ithe  relations  holding  between  natural  entities  are 
/themselves  natural  entities,  namely  they  are  also  factors 
of  fact,  there  for  sense-awareness.  Accordingly  the 
structure  of  the  natural  complex  can  never  be  com- 
pleted in  thought,  just  as  the  factors  of  fact  can  never 
be  exhausted  in  sense-awareness.  Unexhaustiveness  is 
an  essential  character  of  our  knowledge  of  nature.  Also 
nature  does  not  exhaust  the  matter  for  thought,  namely 
there  are  thoughts  which  would  not  occur  in  any  homo- 
geneous thinking  about  nature. 

The  question  as  to  whether  sense-perception  involves 
thought  is  largely  verbal.  If  sense-perception  involves 
a  cognition  of  individuality  abstracted  from  the  actual 
position  of  the  entity  as  a  factor  in  fact,  then  it  un- 
doubtedly does  involve  thought.  But  if  it  is  conceived 
as  sense-awareness  of  a  factor  in  fact  competent  to 
evoke  emotion  and  purposeful  action  without  further 
cognition,  then  it  does  not  involve  thought.  In  such  a 
case  the  terminus  of  the  sense-awareness  is  something 
for  mind,  but  nothing  for  thought.  The  sense-perception 
of  some  lower  forms  of  life  may  be  conjectured  to 
approximate  to  this  character  habitually.  Also  occasion- 
ally our  own  sense-perception  in  moments  when  thought- 
activity  has  been  lulled  to  quiescence  is  not  far  off  the 
attainment  of  this  ideal  limit. 

The  process  of  discrimination  in  sense-awareness  has 
two  distinct  sides.  There  is  the  discrimination  of  fact 
into  parts,  and  the  discrimination  of  any  part  of  fact  as 
exhibiting  relations  to  entities  which  are  not  parts  of 
fact  though  they  are  ingredients  in  it.  Namely  the 
immediate  fact  for  awareness  is  the  whole  occurrence 
of  nature.  It  is  nature  as  an  event^^resent  for  sense- 
awareness,  and  essentially  passing.  There  is  no  holding 


I]  NATURE  AND  THOUGHT  15 

nature  still  and  looking  at  it.  We  cannot  redouble  our 
efforts  to  improve  our  knowledge  of  the  terminus  of  our 
present  sense-awareness;  it  is  our  subsequent  oppor- 
tunity in  subsequent  sense-awareness  which  gains  the 
benefit  of  our  good  resolution.  Thus  the  ultimate  fact 
for  sense-awareness  is  an  event.  This  whole'  event  is 
discriminated  by  us  into  partial  events.  We  are  aware 
of  an  event  which  is  our  bodily  life,  of  an  event  which  is 
the  course  of  nature  within  this  room,  and  of  a  vaguely 
perceived  aggregate  of  other  partial  events.  This  is  the 
discrimination  in  sense-awareness  of  fact  into  parts. 

I  shall  use  the  term  *part'  in  the  arbitrarily  limited 
sense  of  an  event  which  is  part  of  the  whole  fact  dis- 
closed in  awareness. 

Sense-awareness  also  yields  to  us  other  factors  in 
nature  which  are  not  events.  For  example,  sky-blue  is 
seen  as  situated  in  a  certain  event.  This  relation  of 
situation  requires  further  discussion  which  is  postponed 
to  a  later  lecture.  My  present  point  is  that  sky-blue  is 
found  in  nature  with  a  definite  implication  in  events, 
but  is  not  an  event  itself.  Accordingly  in  addition  to 
events,  there  are  other  factors  in  nature  directly  dis- 
closed to  us  in  sense-awareness.  The  conception  in 
thought  of  all  the  factors  in  nature  as  distinct  entities 
with  definite  natural  relations  is  what  I  have  in  another 
place^  called  the  *  diversification  of  nature.' 

There  is  one  general  conclusion  to  be  drawn  from  the 
foregoing  discussion.  It  is  that  the  first  task  of  a  philo- 
sophy of  science  should  be  some  general  classification  of 
the  entities  disclosed  to  us  in  sense-perception. 

Among  the  examples  of  entities  in  addition  to  *  events ' 
which  we  have  used  for  the  purpose  of  illustration  are 
^  Cf.  Enquiry. 


M 


i6  THE  CONCEPT  OF  NATURE  [ch. 

the  buildings  of  Bedford  College,  Homer,  and  sky-blue. 
Evidently  these  are  very  different  sorts  of  things ;  and  it 
is  likely  that  statements  which  are  made  about  one  kind 
of  entity  will  not  be  true  about  other  kinds.  If  human 
thought  proceeded  with  the  orderly  method  which 
abstract  logic  would  suggest  to  it,  we  might  go  further 
and  say  that  a  classification  of  natural  entities  should  be 
the  first  step  in  science  itself.  Perhaps  you  will  be 
inclined  to  reply  that  this  classification  has  already  been 
effected,  and  that  science  is  concerned  with  the  ad- 
ventures of  material  entities  in  space  and  time. 

The  history  of  the  doctrine  of  matter  has  yet  to  be 
written.  It  is  the  history  of  the  influence  of  Greek 
philosophy  on  science.  That  influence  has  issued  in 
one  long  misconception  of  the  metaphysical  status  of 
natural  entities.  The  entity  has  been  separated  from  the 
factor  which  is  the  terminus  of  sense-awareness.  It  has 
become  the  substratum  for  that  factor,  and  the  factor 

J  has  been  degraded  into  an  attribute  of  the  entity.  In 
phis  way  a  distinction  has  been  imported  into  nature 
which  is  in  truth  no  distinction  at  all.  A  natural  entity 
is  merely  a  factor  of  fact,  considered  in  itself.  Its  dis- 
connexion from  the  complex  of  fact  is  a  mere  abstraction. 
^  |It  is  not  the  substratum  of  the  factor,  bixLllie-AcerjL 
factor  itself  as  bared  in  thought  Thus  what  is  a  mere 
(procedure  of  mind  in  the  translation  of  sense-awareness 
into  discursive  knowledge  has  been  transmuted  into  a 
fundamental  character  of  nature.  In  this  way  matter 
has  emerged  as  being  the  metaphysical  substratum  of 
its  properties,  and  the  course  of  nature  is  interpreted 
as  the  history  of  matter. 

Plato  and  Aristotle  found  Greek  thought  preoccupied 
with  the  quest  for  the  simple  substances  in  terms  of 


I]  NATURE  AND  THOUGHT  17 

which  the  course  of  events  could  be  expressed.  We 
may  formulate  this  state  of  mind  in  the  question,  What 
is  nature  made  of?  The  answers  which  their  genius 
gave  to  this  question,  and  more  particularly  the  con- 
cepts which  underlay  the  terms  in  which  they  framed 
their  answers,  have  determined  the  unquestioned  pre- 
suppositions as  to  time,  space  and  matter  which  have 
reigned  in  science. 

In  Plato  the  forms  of  thought  are  more  fluid  than  in 
Aristotle,  and  therefore,  as  I  venture  to  think,  the  more 
valuable.  Their  importance  consists  in  the  evidence 
they  yield  of  cultivated  thought  about  nature  before  it 
had  been  forced  into  a  uniform  mould  by  the  long 
tradition  of  scientific  philosophy.  For  example  in  the 
Timaeus  there  is  a  presupposition,  somewhat  vaguely 
expressed,  of  a  distinction  between  the  general  becoming 
of  nature  and  the  measurable  time  of  nature.  In  a  later 
lecture  I  have  to  distinguish  between  what  I  call  the 
passage  of  nature  and  particular  time-systems  which 
exhibit  certain  characteristics  of  that  passage.  I  will  not 
go  so  far  as  to  claim  Plato  in  direct  support  of  this 
doctrine,  but  I  do  think  that  the  sections  of  the  Timaeus 
which  deal  with  time  become  clearer  if  my  distinction 
is  admitted. 

This  is  however  a  digression.  I  am  now  concerned 
with  the  origin  of  the  scientific  doctrine  of  matter  in 
Greek  thought.  In  the  Timaeus  Plato  asserts  that  nature 
is  made  of  fire  and  earth  with  air  and  water  as  inter- 
mediate between  them,  so  that  *  as  fire  is  to  air  so  is  air 
to  water,  and  as  air  is  to  water  so  is  water  to  earth.'  He 
also  suggests  a  molecular  hypothesis  for  these  four 
elements.  In  this  hypothesis  everything  depends  on  the 
shape  of  the  atoms ;  for  earth  it  is  cubical  and  for  fire 

W.  N.  2 


i8  THE  CONCEPT  OF  NATURE  [ch. 

it  is  pyramidal.  To-day  physicists  are  again  discussing 

the  structure  of  the  atom,  and  its  shape  is  no  sHght 

factor  in  that  structure.  Plato's  guesses  read  much  more 

[fantastically  than  does  Aristotle's  systematic  analysis; 

but  in  some  ways  they  are  more  valuable.  The  main 

outline  of  his  ideas  is  comparable  with  that  of  modern 

j science.    It  embodies  concepts  which  any  theory  of 

/natural  philosophy  must  retain  and  in  some  sense  must 

/  explain.    Aristotle   asked   the   fundamental   question, 

f  What  do  we  mean  by  *  substance '  .^   Here  the  reaction 

between  his  philosophy  and  his   logic  worked  very 

unfortunately.    In  his  logic,  the  fundamental  type  of 

affirmative  proposition  is  the  attribution  of  a  predicate 

Ito  a  subject.  Accordingly,  amid  the  many  current  uses 

/of  the  term  *  substance '  which  he  analyses,  he  emphasises 

/  its  meaning  as  *  the  ultimate  substratum  which  is  no 

I  longer  predicated  of  anything  else.' 

The  unquestioned  acceptance  of  the  Aristotelian  logic 
has  led  to  an  ingrained  tendency  to  postulate  a  sub- 
stratum for  whatever  is  disclosed  in  sense-awareness, 
namely,  to  look  below  what  we  are  aware  of  for  the 
substance  in  the  sense  of  the  *  concrete  thing.'  This 
is  the  origin  of  the  modern  scientific  concept  of  matter 
and  of  ether,  namely  they  are  the  outcome  of  this 
insistent  habit  of  postulation. 

Accordingly  ether  has  been  invented  by  modern 
science  as  the  substratum  of  the  events  which  are 
spread  through  space  and  time  beyond  the  reach  of 
ordinary  ponderable  matter.  Personally,  I  think  that 
predication  is  a  muddled  notion  confusing  many  different 
relations  under  a  convenient  common  form  of  speech. 
For  example,  I  hold  that  the  relation  of  green  to  a  blade 
of  grass  is  entirely  different  from  the  relation  of  green 


I]  NATURE  AND  THOUGHT  19 

to  the  event  which  is  the  Hfe  history  of  that  blade  for 
some  short  period,  and  is  different  from  the  relation 
of  the  blade  to  that  event.  In  a  sense  I  call  the 
event  the  situation  of  the  green,  and  in  another  sense 
it  is  the  situation  of  the  blade.  Thus  in  one  sense  the 
blade  is  a  character  or  property  which  can  be  predi- 
cated of  the  situation,  and  in  another  sense  the  green 
is  a  character  or  property  of  the  same  event  which 
is  also  its  situation.  In  this  way  the  predication  of 
properties  veils  radically  different  relations  between 
entities. 

Accordingly  *  substance,'  which  is  a  correlative  term 
to  '  predication,'  shares  in  the  ambiguity.  If  we  are  to 
look  for  substance  anywhere,  I  should  find  it  in  events 
which  are  in  some  sense  the  ultimate  substance  of 
nature. 

Matter,  in  its  modern  scientific  sense,  is  a  return  to 
the  Ionian  effort  to  find  in  space  and  time  some  stuff 
which  composes  nature.  It  has  a  more  refined  signi- 
fication than  the  early  guesses  at  earth  and  water  by 
reason  of  a  certain  vague  association  with  the  Aristotelian 
idea  of  substance. 

Earth,  water,  air,  fire,  and  matter,  and  finally  ether 
are  related  in  direct  succession  so  far  as  concerns  their 
postulated  characters  of  ultimate  substrata  of  nature. 
They  bear  witness  *to  the  undying  vitality  of  Greek 
philosophy  in  its  search  for  the  ultimate  entities  which 
are  the  factors  of  the  fact  disclosed  in  sense-awareness. 
This  search  is  the  origin  of  science. 

The  succession  of  ideas  starting  from  the  crude 
guesses  of  the  early  Ionian  thinkers  and  ending  in  the 
nineteenth  century  ether  reminds  us  that  the  scientific 
doctrine  of  matter  is  really  a  hybrid  through  which 


Af.'S 


V 


^r 


20  THE  CONCEPT  OF  NATURE  [ch. 

philosophy  passed  on  its  way  to  the  refined  Aristotelian 
concept  of  substance  and  to  which  science  returned  as 
it  reacted  against  philosophic  abstractions.  Earth,  fire, 
and  water  in  the  Ionic  philosophy  and  the  shaped 
elements  in  the  Timaeus  are  comparable  to  the  matter 
and  ether  of  modern  scientific  doctrine.  But  substance 
represents  the  final  philosophic  concept  of  the  sub- 
stratum which  underlies  any  attribute.  Matter  (in  the 
scientific  sense)  is  already  in  space  and  time.  Thus 
matter  represents  the  refusal  to  think  away  spatial  and 
temporal  characteristics  and  to  arrive  at  the  bare  con- 
cept of  an  individual  entity.  It  is  this  refusal  which  has 
caused  the  muddle  of  importing  the  mere  procedure  of 
thought  into  the  fact  of  nature.  The  entity,  bared  of 
all  characteristics  except  those  of  space  and  time,  has  ac- 
quired a  physical  status  as  the  ultimate  texture  of  nature ; 
so  that  the  course  of  nature  is  conceived  as  being  merely 
the  fortunes  of  matter  in  its  adventure  through  space. 
Thus  the  origin  of  the  doctrine  of  matter  is  the  out- 
come of  uncritical  acceptance  of  space  and  time  as 
external  conditions  for  natural  existence.  By  this  I  do 
not  mean  that  any  doubt  should  be  thrown  on  facts  of 
space  and  time  as  ingredients  in  nature.  What  I  do 
mean  is  'the  unconscious  presupposition  of  space  and 
time  as  being  that  within  which  nature  is  set.'  This  is 
exactly  the  sort  of  presupposition  which  tinges  thought 
in  any  reaction  against  the  subtlety  of  philosophical 
I  criticism.  My  theory  of  the  formation  of  the  scientific 
I  doctrine  of  matter  is  that  first  philosophy  illegitimately 
transformed  the  bare  entity,  which  is  simply  an  ab- 
straction necessary  for  the  method  of  thought,  into 
the  metaphysical  substratum  of  these  factors  in  nature 
which  in  various  senses  are  assigned  to  entities  as  their 


I]  NATURE  AND  THOUGHT  21 

attributes ;  and  that,  as  a  second  step,  scientists  (includ- 
ing philosophers  who  were  scientists)  in  conscious  or 
unconscious  ignoration  of  philosophy  presupposed  this 
substratum,  qua  substratum  for  attributes,  as  never- 
theless in  time  and  space. 

This  is  surely  a  muddle.  The  whole  being  of  substance 
is  as  a  substratum  for  attributes.  Thus  time  and  space 
should    be    attributes    of   the    substance.    This    they 
palpably  are  not,  if  the  matter  be  the  substance  of 
nature,  since  it  is  impossible  to  express  spatio-temporal 
truths  without  having  recourse  to  relations  involving 
relata  other  than  bits  of  matter.    I  waive  this  point 
however,  and  come  to  another.   It  is  not  the  substance  f  ^'^^ 
whiclL is _in_ space ^  but  the  attributes.  What  we  find  in/ 
space  are  the  red  of  the  rose  and  the  smell  of  the  jasmine/ 
and  the  noise  of  cannon.  We  have  all  told  our  dentistsi 
where  our  toothache  is.  Thus  space  is  not  a  relatioiJ    , 
between  substances,  but  between  attributes. 

Thus  even  if  you  admit  that  the  adherents  of  sub- 
stance can  be  allowed  to  conceive  substance  as  matter, 
it  is  a  fraud  to  slip  substance  into  space  on  the  plea 
that  space  expresses  relations  between  substances.   On 
the  face  of  it  space  has  nothing  to  do  with  substances, 
but  only  with  their  attributes.    What  I  mean  is,  that 
if  you  choose — as  I  think  wrongly — ^to  construe  our  ex- 
perience of  nature  as  an  awareness  of  the  attributes  of 
substances,  we  are  by  this  theory  precluded  from  finding 
any  analogous  direct  relations  between  substances  as 
disclosed  in  our  experience.    What  we  do  find  are  I 
relations  between  the  attributes  of  substances.  Thus  if  \ 
matter  is  looked  on  as  substance  in  space,  the  space  in  \ 
which  it  finds  itself  has  very  little  to  do  with  the  space   j 
of  our  experience. 


22  THE  CONCEPT  OF  NATURE  [ch. 

The  above  argument  has  been  expressed  in  terms  of 
the  relational  theory  of  space.  But  if  space  be  absolute 
— ^namely,  if  it  have  a  being  independent  of  things  in  it 
— ^the  course  of  the  argument  is  hardly  changed.  For 
things  in  space  must  have  a  certain  fundamental  relation 
to  space  which  we  will  call  occupation.  Thus  the  ob- 
jection that  it  is  the  attributes  which  are  observed  as 
related  to  space,  still  holds. 

The  scientific  doctrine  of  matter  is  held  in  conjunc- 
tion with  an  absolute  theory  of  time.  The  same  argu- 
ments apply  to  the  relations  between  matter  and  time 
as  apply  to  the  relations  between  space  and  matter. 
There  is  however  (in  the  current  philosophy)  a  difference 
in  the  connexions  of  space  with  matter  from  those  of 
time  with  matter,  which  I  will  proceed  to  explain. 

Space  is  not  merely  an  ordering  of  material  entities 
so  that  any  one  entity  bears  certain  relations  to  other 
material  entities.  The  occupation  of  space  impresses  a 
certain  character  on  each  material  entity  in  itself.  By 
reason  of  its  occupation  of  space  matter  has  extension. 
By  reason  of  its  extension  each  bit  of  matter  is  divisible 
into  parts,  and  each  part  is  a  numerically  distinct 
entity  from  every  other  such  part.  Accordingly  it 
would  seem  that  every  material  entity  is  not  really  one 
entity.  It  is  an  essential  multiplicity  of  entities.  There 
seems  to  be  no  stopping  this  dissociation  of  matter  into 
multiplicities  short  of  finding  each  ultimate  entity 
occupying  one  individual  point.  This  essential  multi- 
plicity of  material  entities  is  certainly  not  what  is  meant 
by  sciep^,  nor  does  it  correspond  to  anything  disclosed 
in  sense-awareness.  It  is  absolutely  necessary  that  at 
a  certain  stage  in  this  dissociation  of  matter  a  halt  should 
be  called,  and  that  the  material  entities  thus  obtained 


I]  NATURE  AND  THOUGHT  23 

should  be  treated  as  units.  The  stage  of  arrest  may  be 
arbitrary  or  may  be  set  by  the  characteristics  of  nature ; 
but  all  reasoning  in  science  ultimately  drops  its  space- 
analysis  and  poses  to  itself  the  problem,  '  Here  is  one 
material  entity,  what  is  happening  to  it  as  a  unit 
entity?'  Yet  this  material  entity  is  still  retaining  its 
extension,  and  as  thus  extended  is  a  mere  multiplicity. 
Thus  there  is  an  essential  atomic  property  in  nature 
which  is  independent  of  the  dissociation  of  extension. 
There  is  something  which  in  itself  is  one,  and  which  is 
more  than  the  logical  aggregate  of  entities  occupying 
points  within  the  volume  which  the  unit  occupies. 
Indeed  we  may  well  be  sceptical  as  to  these  ultimate 
entities  at  points,  and  doubt  whether  there  are  any  such 
entities  at  all.  They  have  the  suspicious  character  thati 
we  are  driven  to  accept  them  by  abstract  logic  and  not! 
by  observed  fact.  ' 

Time  (in  the  current  philosophy)  does  not  exert  the 
same  disintegrating  effect  on  matter  which  occupies  it. 
If  matter  occupies  a  duration  of  time,  the  whole  matter 
occupies  every  part  of  that  duration.  Thus  the  connexion 
between  matter  and  time  differs  from  the  connexion 
between  matter  and  space  as  expressed  in  current 
scientific  philosophy.  There  is  obviously  a  greater 
difficulty  in  conceiving  time  as  the  outcome  of  relations 
between  different  bits  of  matter  than  there  is  in  the 
analogous  conception  of  space.  At  an  instant  distinct 
volumes  of  space  are  occupied  by  distinct  bits  of  matter. 
Accordingly  there  is  so  far  no  intrinsic  difficulty  in 
conceiving  that  space  is  merely  the  resultant  of  relations 
between  the  bits  of  matter.  But  in  the  one-dimensional 
time  the  same  bit  of  matter  occupies  different  portions 
of  time.  Accordingly  time  would  have  to  be  expressible 


24  THE  CONCEPT  OF  NATURE  [ch. 

in  terms  of  the  relations  of  a  bit  of  matter  with  itself. 
My  own  view  is  a  belief  in  the  relational  theory  both  of 
space  and  of  time,  and  of  disbelief  in  the  current  form 
of  the  relational  theory  of  space  which  exhibits  bits 

I  of  matter  as  the  relata  for  spatial  relations.  The  true 
relata  are  events.  The  distinction  which  I  have  just 
pointed  out  between  time  and  space  in  their  connexion 
with  matter  makes  it  evident  that  any  assimilation  of 
time  and  space  cannot  proceed  along  the  traditional  line 
of  taking  matter  as  a  fundamental  element  in  space- 
formation. 

The  philosophy  of  nature  took  a  wrong  turn  during 
its  development  by  Greek  thought.  This  erroneous 
presupposition  is  vague  and  fluid  in  Plato's  Timaeus. 
The  general  groundwork  of  the  thought  is  still  un- 
committed and  can  be  construed  as  merely  lacking  due 
explanation  and  the  guarding  emphasis.  But  in 
Aristotle's  exposition  the  current  conceptions  were 
hardened  and  made  definite  so  as  to  produce  a  faulty 
analysis  of  the  relation  between  the  matter  and  the  form 
of  nature  as  disclosed  in  sense-awareness.  In  this  phrase 
the  term  'matter'  is  not  used  in  its  scientific  sense. 

I  will  conclude  by  guarding  myself  against  a  mis- 
apprehension. It  is  evident  that  the  current  doctrine  of 
matter  enshrines  some  fundamental  law  of  nature.  Any 
simple  illustration  will  exemplify  what  I  mean.  For 
example,  in  a  museum  some  specimen  is  locked  securely 
in  a  glass  case.  It  stays  there  for  years :  it  loses  its  colour, 
and  perhaps  falls  to  pieces.  But  it  is  the  same  specimen ; 
and  the  same  chemical  elements  and  the  same  quantities 
of  those  elements  are  present  within  the  case  at  the  end 
as  were  present  at  the  beginning.  Again  the  engineer 
and  the  astronomer  deal  with  the  motions  of  real  per- 


I]  NATURE  AND  THOUGHT  25 

manences  in  nature.  Any  theory  of  nature  which  for 
one  moment  loses  sight  of  these  great  basic  facts  of 
experience  is  simply  silly.  But  it  is  permissible  to  point 
out  that  the  scientific  expression  of  these  facts  has  be- 
come entangled  in  a  maze  of  doubtful  metaphysics; 
and  that,  when  we  remove  the  metaphysics  and  start 
afresh  on  an  unprejudiced  survey  of  nature,  a  new  light 
is  thrown  on  many  fundamental  concepts  which  domi- 
nate science  and  guide  the  progress  of  research. 


^ 


CHAPTER  II 

THEORIES  OF  THE  BIFURCATION 
OF  NATURE 

j  In  my  previous  lecture  I  criticised  the  concept  of  matter 
»  as  the  substance  whose  attributes  we  perceive.  This  way 
of  thinking  of  matter  is,  I  think,  the  historical  reason 
for  its  introduction  into  science,  and  is  still  the  vague 
view  of  it  at  the  background  of  our  thoughts  which 
makes  the  current  scientific  doctrine  appear  so  obvious. 
Namely  we  conceive  ourselves  as  perceiving  attributes 
of  things,  and  bits  of  matter  are  the  things  whose 
attributes  we  perceive. 

In  the  seventeenth  century  the  sweet  simplicity  of 
this  aspect  of  matter  received  a  rude  shock.  The  trans- 
mission doctrines  of  science  were  then  in  process  of 
elaboration  and  by  the  end  of  the  century  were  un- 
questioned, though  their  particular  forms  have  since 
been  modified.  The  establishment  of  these  transmission 
theories  marks  a  turning  point  in  the  relation  between 
science  and  philosophy.  The  doctrines  to  which  I  am 
especially  alluding  are  the  theories  of  light  and  sound. 
I  have  no  doubt  that  the  theories  had  been  vaguely 
floating  about  before  as  obvious  suggestions  of  common 
sense;  for  nothing  in  thought  is  ever  completely  new. 
But  at  that  epoch  they  were  systematised  and  made 
exact,  and  their  complete  consequences  were  ruthlessly 
II  deduced.  It  is  the  establishment  of  this  procedure  of 
II  taking  the  consequences  seriously  which  marks  the 
||real  discovery  of  a  theory.  Systematic  doctrines  of 
light  and  sound  as  being  something  proceeding  from 


CH.ii]  THEORIES  OF  BIFURCATION  OF  NATURE  27 

the  emitting  bodies  were  definitely  established,  and  in 
particular  the  connexion  of  Hght  with  colour  was  laid 
bare  by  Newton. 

The  result  completely  destroyed  the  simplicity  of  the 
*  substance  and  attribute'  theory  of  perception.  What 
we  see  depends  on  the  light  entering  the  eye.  Further- 
more we  do  not  even  perceive  what  enters  the  eye.  The 
things  transmitted  are  waves  or — as  Newton  thought — 
minute  particles,  and  the  things  seen  are  colours.  Locke 
met  this  difficulty  by  a  theory  of  primary  and  secondary 
qualities.  Namely,  there  are  some  attributes  of  the 
matter  which  we  do  perceive.  These  are  the  primary 
qualities,  and  there  are  other  things  which  we  perceive, 
such  as  colours,  which  are  not  attributes  of  matter,  but 
are  perceived  by  us  as  if  they  were  such  attributes. 
These  are  the  secondary  qualities  of  matter. 

Why  should  we  perceive  secondary  qualities.'^  It 
seems  an  extremely  unfortunate  arrangement  that  we 
should  perceive  a  lot  of  things  that  are  not  there.  Yet 
this  is  what  the  theory  of  secondary  qualities  in  fact 
comes  to.  There  is  now  reigning  in  philosophy  and  in 
science  an  apathetic  acquiescence  in  the  conclusion  that 
no  coherent  account  can  be  given  of  nature  as  it  is 
disclosed  to  us  in  sense-awareness,  without  dragging  in 
its  relations  to  mind.  The  modern  account  of  nature  is 
not,  as  it  should  be,  merely  an  account  of  what  the  mind 
knows  of  nature ;  but  it  is  also  confused  with  an  account 
of  what  nature  does  to  the  mind.  The  result  has  been 
disastrous  both  to  science  and  to  philosophy,  but  chiefly 
to  philosophy.  It  has  transformed  the  grand  question 
of  the  relations  between  nature  and  mind  into  the  petty 
form  of  the  interaction  between  the  human  body  and 
mind. 


• 


28  THE  CONCEPT  OF  NATURE  [ch. 

Berkeley's  polemic  against  matter  was  based  on  this 
confusion  introduced  by  the  transmission  theory  of 
light.  He  advocated,  rightly  as  I  think,  the  abandon- 
ment of  the  doctrine  of  matter  in  its  present  form.  He 
had  however  nothing  to  put  in  its  place  except  a  theory 
of  the  relation  of  finite  minds  to  the  divine  mind. 

But  we  are  endeavouring  in  these  lectures  to  limit 
ourselves  to  nature  itself  and  not  to  travel  beyond 
entities  which  are  disclosed  in  sense-awareness. 

Percipience  in  itself  is  taken  for  granted.  We  consider 
indeed  conditions  for  percipience,  but  only  so  far  as 
those  conditions  are  among  the  disclosures  of  percep- 
tion. We  leave  to  metaphysics  the  synthesis  of  the 
knower  and  the  known.  Some  further  explanation  and 
defence  of  this  position  is  necessary,  if  the  line  of  argu- 
ment of  these  lectures  is  to  be  comprehensible. 

The  immediate  thesis  for  discussion  is  that  any  meta- 
physical interpretation  is  an  illegitimate  importation  into 
the  philosophy  of  natural  science.  By  a  metaphysical 
interpretation  I  mean  any  discussion  of  the  how  (beyond 
nature)  and  of  the  why  (beyond  nature)  of  thought  and 
sense-awareness.  In  the  philosophy  of  science  we  seek 
the  general  notions  which  apply  to  nature,  namely,  to 
what  we  are  aware  of  in  perception.  It  is  the  philosophy 
of  the  thing  perceived,  and  it  should  not  be  confused 
with  the  metaphysics  of  reality  of  which  the  scope 
embraces  both  perceiver  and  perceived.  No  perplexity 
concerning  the  object  of  knowledge  can  be  solved  by 
saying  that  there  is  a  mind  knowing  it^. 

In  other  words,  the  ground  taken  is  this:  sense- 
awareness  is  an  awareness  of  something.  What  then  is 
the  general  character  of  that  something  of  which  we 
1  Cf.  Enquiry,  preface. 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  29 

are  aware?  We  do  not  ask  about  the  percipient  or 
about  the  process,  but  about  the  perceived.  I  emphasise 
this  point  because  discussions  on  the  philosophy  of 
science  are  usually  extremely  metaphysical — in  my 
opinion,  to  the  great  detriment  of  the  subject. 

The  recourse  to  metaphysics  is  like  throwing  a  match 
into  the  powder  magazine.  It  blows  up  the  whole  arena. 
This  is  exactly  what  scientific  philosophers  do  when 
they  are  driven  into  a  corner  and  convicted  of  inco- 
herence. They  at  once  drag  in  the  mind  and  talk  of 
entities  in  the  mind  or  out  of  the  mind  as  the  case  may 
be.  For  natural  philosophy  everything  perceived  is  in 
nature.  We  n^ay  not  pick  and  choose.  For  us  the  red 
glow  of  the  sunset  should  be  as  much  part  of  nature  as 
are  the  molecules  and  electric  waves  by  which  men  of 
/science  would  explain  the  phenomenon.  It  is  for  natural/^  f 
philosophy  to  analyse  how  these  various  elements  of  j^.  \W^ia 
I  nature  are  connected.  A^'^t-^t^^/iw  M 

In  making  this  demand  I  conceive  myself  as  adopting  V^^iJ^ 
our  immediate  instinctive  attitude  towards  perceptual 
knowledge  which  is  only  abandoned  under  the  influence 
of  theory.  We  are  instinctively  willing  to  believe  that  by 
due  attention,  more  can  be  found  in  nature  than  that 
which  is  observed  at  first  sight.  But  we  will  not  be 
content  with  less.  What  we  ask  from  the  philosopliy  of 
science  is  some  account  of  the  coherence  of  things 
perceptively  known . 

This  means  a  refusal  to  countenance  any  theory  of 
psychic  additions  to  the  object  known  in  perception. 
For  example,  what  is  given  in  perception  is  the  green 
grass.  This  is  an  object  which  we  know  as  an  ingredient 
in  nature.  The  theory  of  psychic  additions  would  treat 
the  greenness  as  a  psychic  addition  furnished  by  the 


U*^ 

^ 


^  MiCinAl     ^<dcVsii    fKACiJUftJi  I 


I 


30  THE  CONCEPT  OF  NATURE  [ch. 

perceiving  mind,  and  would  leave  to  nature  merely  the 
molecules  and  the  radiant  energy  which  influence  the 
mind  towards  that  perception.  My  argument  is  that  this 
dragging  in  of  the  mind  as  making  additions  of  its  own 
to  the  thing  posited  for  knowledge  by  sense-awareness 
is  merely  a  way  of  shirking  the  problem  of  natural 
philosophy.  That  problem  is  to  discuss  the  relations 
inter  se  of  things  known,  abstracted  from  the  bare  fact 
that  they  are  known.  Natural  philosophy  should  never 
ask,  what  is  in  the  mind  and  what  is  in  nature.  To  do  so 
is  a  confession  that  it  has  failed  to  express  relations 
between  things  perceptively  known,  namely  to  express 
those  natural  relations  whose  expression  is  natural 
philosophy.  It  may  be  that  the  task  is  too  hard  for  us, 
that  the  relations  are  too  complex  and  too  various  for 
our  apprehension,  or  are  too  trivial  to  be  worth  the 
trouble  of  exposition.  It  is  indeed  true  that  we  have 
gone  but  a  very  small  way  in  the  adequate  formulation 
of  such  relations.  But  at  least  do  not  let  us  endeavour 
to  conceal  failure  under  a  theory  of  the  byplay  of  the 
perceiving  mind. 

What  I  am  essentially  protesting  against  is  the  bi- 
furcation of  nature  into  two  systems  of  reality,  which, 
in  so  far  as  they  are  real,  are  real  in  different  senses. 
One  reality  would  be  the  entities  such  as  electrons  which 
are  the  study  of  speculative  physics.  This  would  be  the 
reality  which  is  there  for  knowledge ;  although  on  this 
theory  it  is  never  known.  For  what  is  known  is  the 
other  sort  of  reality,  which  is  the  byplay  of  the  mind. 
Thus  there  would  be  two  natures,  one  is  the  conjecture 
and  the  other  is  the  dream. 

Another  way  of  phrasing  this  theory  which  I  am 
arguing  against  is  to  bifurcate  nature  into  two  divisions, 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  31 

namely  into  the  nature  apprehended  in  awareness  and 
the  nature  which  is  the  cause  of  awareness.  The  nature 
which  is  the  fact  apprehended  in  awareness  holds  within 
it  the  greenness  of  the  trees,  the  song  of  the  birds,  the 
warmth  of  the  sun,  the  hardness  of  the  chairs,  and  the 
feel  of  the  velvet.  The  nature  which  is  the  cause  of 
awareness  is  the  conjectured  system  of  molecules  and 
electrons  which  so  affects  the  mind  as  to  produce  the 
awareness  of  apparent  nature.  The  meeting  point  of 
these  two  natures  is  the  mind,  the  causal  nature  being 
influent  and  the  apparent  nature  being  effluent. 

There  are  four  questions  which  at  once  suggest 
themselves  for  discussion  in  connexion  with  this  bi- 
furcation theory  of  nature.  They  concern  (i)  causality, 
(ii)  time,  (iii)  space,  and  (iv)  delusions.  These  questions 
are  not  really  separable.  They  merely  constitute  four 
distinct  starting  points  from  which  to  enter  upon  the 
discussion  of  the  theory. 

Causal  nature  is  the  influence  on  the  mind  which  is 
the  cause  of  the  effluence  of  apparent  nature  from  the 
mind.  This  conception  of  causal  nature  is  not  to  be 
confused  with  the  distinct  conception  of  one  part  of 
nature  as  being  the  cause  of  another  part.  For  example, 
the  burning  of  the  fire  and  the  passage  of  heat  from  it 
through  intervening  space  is  the  cause  of  the  body,  its 
nerves  and  its  brain,  functioning  in  certain  ways.  But 
this  is  not  an  action  of  nature  on  the  mind.  It  is  an 
interaction  within  nature.  The  causation  involved  in  this 
interaction  is  causation  in  a  different  sense  from  the 
influence  of  this  system  of  bodily  interactions  within 
nature  on  the  alien  mind  which  thereupon  perceives 
redness  and  warmth. 

The   bifurcation  theory   is   an   attempt   to   exhibit 


32  THE  CONCEPT  OF  NATURE  [ch. 

natural  science  as  an  investigation  of  the  cause  of  the 
fact  of  knowledge.  Namely,  it  is  an  attempt  to  exhibit 
apparent  nature  as  an  effluent  from  the  mind  because  of 
causal  nature.  The  whole  notion  is  partly  based  on  the 
implicit  assumption  that  the  mind  can  only  know  that 
which  it  has  itself  produced  and  retains  in  some  sense 
within  itself,  though  it  requires  an  exterior  reason  both 
as  originating  and  as  determining  the  character  of  its 
activity.  But  in  considering  knowledge  we  should  wipe 
out  all  these  spatial  metaphors,  such  as  *  within  the 
mind'  and  *  without  the  mind.'  Knowledge  is  ultimate. 
There  can  be  no  explanation  of  the  *  why '  of  knowledge ; 
we  can  only  describe  the  *  what '  of  knowledge.  Namely 
we  can  analyse  the  content  and  its  internal  relations, 
but  we  cannot  explain  why  there  is  knowledge.  Thus 
causal  nature  is  a  metaphysical  chimera ;  though  there  is 
need  of  a  metaphysics  whose  scope  transcends  the 
limitation  to  nature.  The  object  of  such  a  metaphysical 
science  is  not  to  explain  knowledge,  but  exhibit  in  its 
utmost  completeness  our  concept  of  reality. 

However,  we  must  admit  that  the  causality  theory  of 
nature  has  its  strong  suit.  The  reason  why  the  bifurca- 
tion of  nature  is  always  creeping  back  into  scientific 
philosophy  is  the  extreme  difficulty  of  exhibiting  the 
perceived  redness  and  warmth  of  the  fire  in  one  system 
of  relations  with  the  agitated  molecules  of  carbon  and 
oxygen,  with  the  radiant  energy  from  them,  and  with  the 
various  functionings  of  the  material  body.  Unless  we 
produce  the  all-embracing  relations,  we  are  faced  with  a 
bifurcated  nature ;  namely,  warmth  and  redness  on  one 
side,  and  molecules,  electrons  and  ether  on  the  other 
side.  Then  the  two  factors  are  explained  as  being  re- 
spectively the  cause  and  the  mind's  reaction  to  the  cause. 


ii]   THEORIES  OF  BIFURCATION  OF  NATURE  33 

Time  and  space  would  appear  to  provide  these  all- 
embracing  relations  which  the  advocates  of  the  philo- 
sophy of  the  unity  of  nature  require.  The  perceived 
redness  of  the  fire  and  the  warmth  are  definitely  related 
in  time  and  in  space  to  the  molecules  of  the  fire  and  the 
molecules  of  the  body. 

It  is  hardly  more  than  a  pardonable  exaggeration  to 
say  that  the  determination  of  the  meaning  of  nature 
reduces  itself  principally  to  the  discussion  of  the  charac- 
ter of  time  and  the  character  of  space.  In  succeeding 
lectures  I  shall  explain  my  own  view  of  time  and  space. 
I  shall  endeavour  to  show  that  they  are  abstractions 
from  more  concrete  elements  of  nature,  namely,  from 
events.  The  discussion  of  the  details  of  the  process  of 
abstraction  will  exhibit  time  and  space  as  interconnected, 
and  will  finally  lead  us  to  the  sort  of  connexions  between 
their  measurements  which  occur  in  the  modern  theory 
of  electromagnetic  relativity.  But  this  is  anticipating 
our  subsequent  line  of  development.  At  present  I  wish 
to  consider  how  the  ordinary  views  of  time  and  space 
help,  or  fail  to  help,  in  unifying  our  conception  of  nature. 

First,  consider  the  absolute  theories  of  time  and 
space.  We  are  to  consider  each,  namely  both  time  and 
space,  to  be  a  separate  and  independent  system  of 
entities,  each  system  known  to  us  in  itself  and  for  itself 
concurrently  with  our  knowledge  of  the  events  of 
nature.  Time  is  the  ordered  succession  of  durationless 
instants ;  and  these  instants  are  known  to  us  merely  as 
the  relata  in  the  serial  relation  which  is  the  time- 
ordering  relation,  and  the  time-ordering  relation  is 
merely  known  to  us  as  relating  the  instants.  Namely, 
the  relation  and  the  instants  are  jointly  known  to  us  in 
our  apprehension  of  time,  each  implying  the  other. 

W.  N.  ^ 


34  THE  CONCEPT  OF  NATURE  [ch. 

This  is  the  absolute  theory  of  time.  Frankly,  I  con- 
fess that  it  seems  to  me  to  be  very  unplausible.  I  cannot 
in  my  own  knowledge  find  anything  corresponding  to 
the  bare  time  of  the  absolute  theory.  Time  is  known  to 
me  as  an  abstraction  from  the  passage  of  events.  The 
fundamental  fact  which  renders  this  abstraction  possible 
is  the  passing  of  nature,  its  development,  its  creative 
advance,  and  combined  with  this  fact  is  another  charac- 
teristic of  nature,  namely  the  extensive  relation  between 
events.  These  two  facts,  namely  the  passage  of  events 
and  the  extension  of  events  over  each  other,  are  in  my 
opinion  the  qualities  from  which  time  and  space  originate 
as  abstractions.  But  this  is  anticipating  my  own  later 
speculations. 

Meanwhile,  returning  to  the  absolute  theory,  we  are 
to  suppose  that  time  is  known  to  us  independently  of 
any  events  in  time.  What  happens  in  time  occupies  time. 
This  relation  of  events  to  the  time  occupied,  namely 
this  relation  of  occupation,  is  a  fundamental  relation  of 
nature  to  time.  Thus  the  theory  requires  that  we  are 
aware  of  two  fundamental  relations,  the  time-ordering 
relation  between  instants,  and  the  time-occupation 
relation  between  instants  of  time  and  states  of  nature 
which  happen  at  those  instants. 

There  are  two  considerations  which  lend  powerful 
support  to  the  reigning  theory  of  absolute  time.  In 
the  first  place  time  extends  beyond  nature.  Our  thoughts 
are  in  time.  Accordingly  it  seems  impossible  to  derive 
time  merely  from  relations  between  elements  of  nature. 
For  in  that  case  temporal  relations  could  not  relate 
thoughts.  Thus,  to  use  a  metaphor,  time  would  ap- 
parently have  deeper  roots  in  reality  than  has  nature. 
For  we  can  imagine  thoughts  related  in  time  without 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  35 

any  perception  of  nature.  For  example  we  can  imagine 
one  of  Milton's  angels  with  thoughts  succeeding  each 
other  in  time,  who  does  not  happen  to  have  noticed 
that  the  Almighty  has  created  space  and  set  therein  a 
material  universe.  As  a  matter  of  fact  I  think  that  Milton 
set  space  on  the  same  absolute  level  as  time.  But  that 
need  not  disturb  the  illustration.  In  the  second  place 
it  is  difficult  to  derive  the  true  serial  character  of  time 
from  the  relative  theory.  Each  instant  is  irrevocable.  It 
can  never  recur  by  the  very  character  of  time.  But  if 
on  the  relative  theory  an  instant  of  time  is  simply  the 
state  of  nature  at  that  time,  and  the  time-ordering 
relation  is  simply  the  relation  between  such  states,  then 
the  irrevocableness  of  time  would  seem  to  mean  that 
an  actual  state  of  all  nature  can  never  return.  I  admit 
it  seems  unlikely  that  there  should  ever  be  such  a 
recurrence  down  to  the  smallest  particular.  But 
extreme  unlikeliness  is  not  the  point.  Our  ignorance  is 
so  abysmal  that  our  judgments  of  likeliness  and  un- 
likeliness of  future  events  hardly  count.  The  real  point 
is  that  the  exact  recurrence  of  a  state  of  nature  seems 
merely  unlikely,  while  the  recurrence  of  an  instant  of 
time  violates  our  whole  concept  of  time-order.  The 
instants  of  time  which  have  passed,  are  passed,  and  can 
never  be  again. 

Any  alternative  theory  of  time  must  reckon  with  these 
two  considerations  which  are  buttresses  of  the  absolute 
theory.  But  I  will  not  now  continue  their  discussion. 

The  absolute  theory  of  space  is  analogous  to  the 
corresponding  theory  of  time,  but  the  reasons  for  its 
maintenance  are  weaker.  Space,  on  this  theory,  is  a 
system  of  extensionless  points  which  are  the  relata  in 
space-ordering  relations  which  can  technically  be  com- 

3—2 


36  THE  CONCEPT  OF  NATURE  [ch. 

bined  into  one  relation.  This  relation  does  not  arrange 
the  points  in  one  linear  series  analogously  to  the  simple 
method  of  the  time-ordering  relation  for  instants.  The 
essential  logical  characteristics  of  this  relation  from 
which  all  the  properties  of  space  spring  are  expressed 
by  mathematicians  in  the  axioms  of  geometry.  From 
these  axioms^  as  framed  by  modern  mathematicians 
the  whole  science  of  geometry  can  be  deduced  by  the 
strictest  logical  reasoning.  The  details  of  these  axioms 
do  not  now  concern  us.  The  points  and  the  relations 
are  jointly  known  to  us  in  our  apprehension  of  space, 
each  implying  the  other.  What  happens  in  space, 
occupies  space.  This  relation  of  occupation  is  not 
usually  stated  for  events  but  for  objects.  For  example, 
Pompey's  statue  would  be  said  to  occupy  space,  but  not 
the  event  which  was  the  assassination  of  Julius  Caesar. 
In  this  I  think  that  ordinary  usage  is  unfortunate,  and 
I  hold  that  the  relations  of  events  to  space  and  to  time 
are  in  all  respects  analogous.  But  here  I  am  intruding 
my  own  opinions  which  are  to  be  discussed  in  subse- 
quent lectures.  Thus  the  theory  of  absolute  space 
requires  that  we  are  aware  of  two  fundamental  relations, 
the  space-ordering  relation,  which  holds  between  points, 
and  the  space-occupation  relation  between  points  of 
space  and  material  objects. 

This  theory  lacks  the  two  main  supports  of  the  corre- 
sponding theory  of  absolute  time.  In  the  first  place  space 
does  not  extend  beyond  nature  in  the  sense  that  time 
seems  to  do.  Our  thoughts  do  not  seem  to  occupy  space 
in  quite  the  same  intimate  way  in  which  they  occupy 
time.  For  example,  I  have  been  thinking  in  a  room,  and 

1  Cf.  (for  example)  Projective  Geometry  by  Veblen  and  Young, 
vol.  i.  1 9 10,  vol.  ii.  19 17,  Ginn  and  Company,  Boston,  U.S.A. 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  37 

to  that  extent  my  thoughts  are  in  space.  But  it  seems 
nonsense  to  ask  how  much  volume  of  the  room  they 
occupied,  whether  it  was  a  cubic  foot  or  a  cubic  inch; 
whereas  the  same  thoughts  occupy  a  determinate  dura- 
tion of  time,  say,  from  eleven  to  twelve  on  a  certain  date. 

Thus  whereas  the  relations  of  a  relative  theory  of 
time  are  required  to  relate  thoughts,  it  does  not  seem  so 
obvious  that  the  relations  of  a  relative  theory  of  space 
are  required  to  relate  them.  The  connexion  of  thought 
with  space  seems  to  have  a  certain  character  of  indirect- 
ness which  appears  to  be  lacking  in  the  connexion  of 
thought  with  time. 

Again  the  irrevocableness  of  time  does  not  seem  to 
have  any  parallel  for  space.  Space,  on  the  relative  theory, 
is  the  outcome  of  certain  relations  between  objects 
commonly  said  to  be  in  space ;  and  whenever  there  are 
the  objects,  so  related,  there  is  the  space.  No  difficulty 
seems  to  arise  like  that  of  the  inconvenient  instants  of 
time  which  might  conceivably  turn  up  again  when  we 
thought  that  we  had  done  with  them. 

The  absolute  theory  of  space  is  not  now  generally 
popular.  The  knowledge  of  bare  space,  as  a  system  of 
entities  known  to  us  in  itself  and  for  itself  independently 
of  our  knowledge  of  the  events  in  nature,  does  not  seem 
to  correspond  to  anything  in  our  experience.  Space, 
like  time,  would  appear  to  be  an  abstraction  from  events. 
According  to  my  own  theory  it  only  differentiates 
itself  from  time  at  a  somewhat  developed  stage  of  the 
abstractive  process.  The  more  usual  way  of  expressing 
the  relational  theory  of  space  would  be  to  consider  space 
as  an  abstraction  from  the  relations  between  material 
objects. 

Suppose  now  we  assume  absolute  time  and  absolute 


38  THE  CONCEPT  OF  NATURE  [ch. 

space.  What  bearing  has  this  assumption  on  the  con- 
cept of  nature  as  bifurcated  into  causal  nature  and 
apparent  nature  ?  Undoubtedly  the  separation  between 
the  two  natures  is  now  greatly  mitigated.  We  can  pro- 
vide them  with  two  systems  of  relations  in  common ;  for 
both  natures  can  be  presumed  to  occupy  the  same  space 
and  the  same  time.  The  theory  now  is  this :  Causal  events 
occupy  certain  periods  of  the  absolute  time  and  occupy 
certain  positions  of  the  absolute  space.  These  events 
influence  a  mind  which  thereupon  perceives  certain 
apparent  events  which  occupy  certain  periods  in  the 
absolute  time  and  occupy  certain  positions  of  the 
absolute  space ;  and  the  periods  and  positions  occupied 
by  the  apparent  events  bear  a  determinate  relation  to 
the  periods  and  positions  occupied  by  the  causal  events. 
Furthermore  definite  causal  events  produce  for  the 
mind  definite  apparent  events.  Delusions  are  apparent 
events  which  appear  in  temporal  periods  and  spatial 
positions  without  the  intervention  of  these  causal 
events  which  are  proper  for  influencing  of  the  mind  to 
their  perception. 

The  whole  theory  is  perfectly  logical.  In  these  dis- 
cussions we  cannot  hope  to  drive  an  unsound  theory  to 
a  logical  contradiction.  A  reasoner,  apart  from  mere 
slips,  only  involves  himself  in  a  contradiction  when  he 
is  shying  at  a  reductio  ad  absurdum.  The  substantial 
reason  for  rejecting  a  philosophical  theory  is  the  '  ab- 

jsurdum*  to  which  it  reduces  us.  In  the  case  of  the 
philosophy  of  natural  science  the  '  absurdum '  can  only; 
be  that  our  perceptual  knowledge  has  not  the  character 

;  assigned  to  it  by  the  theory.  If  our  opponent  affirms 
that  his  knowledge  has  that  character,  we  can  only — 
after  making  doubly  sure  that  we  understand  each 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  39 

other — ^agree  to  differ.  Accordingly  the  first  duty  of 
an  expositor  in  stating  a  theory  in  which  he  disbelieves 
is  to  exhibit  it  as  logical.  It  is  not  there  where  his 
trouble  lies. 

Let  me  summarise  the  previously  stated  objections 
to  this  theory  of  nature.  In  the  first  place  it  seeks  for  ^ 
the  cause  of  the  knowledge  "f  the  thing  knowr)  jngtipaH 
qf^  seeking__for  the  character  of  the  thing  known: 
secondly  it  assumes  a  knowledge  of  time  in  itself  apart 
from  events  related  in  time :  thirdly  it  assumes  a  know- 
ledge of  space  in  itself  apart  from  events  related  in 
space.  There  are  in  addition  to  these  objections  other 
flaws  in  the  theory. 

Some  light  is  thrown  on  the  artificial  status  of  causal 
nature  in  this  theory  by  asking,  why  causal  nature  is 
presumed  to  occupy  time  and  space.  This  really  raises 
the  fundamental  question  as  to  what  characteristics 
causal  nature  should  have  in  common  with  apparent 
nature.  Why — on  this  theory — should  the  cause  which 
influences  the  mind  to  perception  have  any  character- 
istics in  common  with  the  eflSuent  apparent  nature.? 
In  particular,  why  should  it  be  in  space  ?  Why  should 
it  be  in  time.^*  And  more  generally.  What  do  we 
know  about  mind  which  would  allow  us  to  infer  any 
particular  characteristics  of  a  cause  which  should  in- 
fluence mind  to  particular  effects } 

The  transcendence  of  time  beyond  nature  gives  some 
slight  reason  for  presuming  that  causal  nature  should 
occupy  time.  For  if  the  mind  occupies  periods  of  time, 
there  would  seem  to  be  some  vague  reason  for  assuming 
that  influencing  causes  occupy  the  same  periods  of 
time,  or  at  least,  occupy  periods  which  are  strictly 
related  to  the  mental  periods.  But  if  the  mind  does  not 


^i 


40  THE  CONCEPT  OF  NATURE  [cH. 

occupy  volumes  of  space,  there  seems  to  be  no  reason 
why  causal  nature  should  occupy  any  volumes  of  space. 
Thus  space  would  seem  to  be  merely  apparent  in  the 
same  sense  as  apparent  nature  is  merely  apparent. 
Accordingly  if  science  is  really  investigating  causes 
which  operate  on  the  mind,  it  would  seem  to  be  entirely 
on  the  wrong  tack  in  presuming  that  the  causes  which 
it  is  seeking  for  have  spatial  relations.  Furthermore 
there  is  nothing  else  in  our  knowledge  analogous  to 
these  causes  which  influence  the  mind  to  perception. 
Accordingly,  beyond  the  rashly  presumed  fact  that  they 
occupy  time,  there  is  really  no  ground  by  which  we  can 
determine  any  point  of  their  character.  They  must 
remain  for  ever  unknown. 

Now  I  assume  as  an  axiom  that  science  is  not  a 
fairy  tale.  It  is  not  engaged  in  decking  out  unknowable 
entities  with  arbitrary  and  fantastic  properties.  What 
then  is  it  that  science  is  doing,  granting  that  it  is 
effecting  something  of  importance }  My  answer  is  that 
it  is  determining  the  character  of  things  known,  namely 
the  character  of  apparent  nature.  But  we  may  drop  the 
term  *  apparent';  for  there  is  but  one  nature,  namely 
the  nature  which  is  before  us  in  perceptual  knowledge. 
The  characters  which  science  discerns  in  nature  are 
subtle  characters,  not  obvious  at  first  sight.  They  are 
relations  of  relations  and  characters  of  characters.  But 
for  all  their  subtlety  they  are  stamped  with  a  certain 
simplicity  which  makes  their  consideration  essential  in 
unravelling  the  complex  relations  between  characters 
of  more  perceptive  insistence. 

The  fact  that  the  bifurcation  of  nature  into  causal  and 
apparent  components  does  not  express  what  we  mean 
by  our  knowledge  is  brought  before  us  when  we  realise 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  41 

our  thoughts  in  any  discussion  of  the  causes  of  our 
perceptions.   For  example,  the  fire  is  burning  and  we ' 
see  a  red  coal.  This  is  explained  in  science  by  radiant^ 
energy  from  the  coal  entering  our  eyes.  But  in  seeking] 
for  such  an  explanation  we  are  not  asking  what  are  the  j 
sort  of  occurrences  which  are  fitted  to  cause  a  mind  to  j 
see  red.  The  chain  of  causation  is  entirely  different.  The 
mind  is  cut  out  altogether.  The  real  question  is,  When 
red  is  found  in  nature,  what  else  is  found  there  also? 
Namely  we  are  asking  for  an  analysis  of  the  accom- 
paniments in  nature  of  the  discovery  of  red  in  nature. 
In  a  subsequent  lecture  I  shall  expand  this  line  of 
thought.  I  simply  draw  attention  to  it  here  in  order  to 
point  out  that  the  wave-theory  of  light  has  not  been 
adoBt£d,hecause^aves  are  just  the  s^rFoLthings  which 
ought  to  make  ajnind  perceive  colours.  This  is  no  part 
oTtKe  evidence  which  has  ever  been  adduced  for  the 
wave-theory,  yet  on  the  causal  theory  of  perception,  it 
is  really  the  only  relevant  part.  In  other  words,  science 
is  not  discussing  the  causes  of  knowledge,  but  the 

coherence  of  knowledge.  The  understanding  which  isli 

sought  by  science  is  an  understanding  of  relations!  i 
within  nature.  •' 

So  far  I  have  discussed  the  bifurcation  of  nature  in 
connexion  with  the  theories  of  absolute  time  and  of 
absolute  space.  My  reason  has  been  that  the  intro- 
duction of  the  relational  theories  only  weakens  the  case 
for  bifurcation,  and  I  wished  to  discuss  this  case  on 
its  strongest  grounds. 

For  instance,  suppose  we  adopt  the  relational  theory 
of  space.  Then  the  space  in  which  apparent  nature  is  set 
is  the  expression  of  certain  relations  between  the  appa- 
rent objects.   It  is  a  set  of  apparent  relations  between 


KjI- 


42  THE  CONCEPT  OF  NATURE  [ch. 

apparent  relata.  Apparent  nature  is  the  dream,  and  the 
apparent  relations  of  space  are  dream  relations,  and  the 
space  is  the  dream  space.  Similarly  the  space  in  which 
causal  nature  is  set  is  the  expression  of  certain  rela- 
tions between  the  causal  objects.  It  is  the  expression 
of  certain  facts  about  the  causal  activity  which  is  going 
on  behind  the  scenes.  Accordingly  causal  space  belongs 
to  a  different  order  of  reality  to  apparent  space.  Hence 
there  is  no  pointwise  connexion  between  the  two  and 
it  is  meaningless  to  say  that  the  molecules  of  the  grass 
are  in  any  place  which  has  a  determinate  spatial  relation 
to  the  place  occupied  by  the  grass  which  we  see.  This 
conclusion  is  very  paradoxical  and  makes  nonsense  of 
all  scientific  phraseology.  The  case  is  even  worse  if  we 
admit  the  relativity  of  time.  For  the  same  arguments 
apply,  and  break  up  time  into  the  dream  time  and  causal 
time  which  belong  to  difl^erent  orders  of  reality. 

I  have  however  been  discussing  an  extreme  form  of 
the  bifurcation  theory.  It  is,  as  I  think,  the  most 
defensible  form.  But  its  very  definiteness  makes  it  the 
more  evidently  obnoxious  to  criticism.  The  intermediate 
form  allows  that  the  nature  we  are  discussing  is  always 
the  nature  directly  known,  and  so  far  it  rejects  the 
bifurcation  theory.  But  it  holds  that  there  are  psychic 
additions  to  nature  as  thus  known,  and  that  these 
additions  are  in  no  proper  sense  part  of  nature.  For 
example,  we  perceive  the  red  billiard  ball  at  its  proper 
time,  in  its  proper  place,  with  its  proper  motion,  with 
its  proper  hardness,  and  with  its  proper  inertia.  But 
its  redness  and  its  warmth,  and  the  sound  of  the  click 
as  a  cannon  is  made  oflr  it  are  psychic  additions,  namely, 
secondary  qualities  which  are  only  the  mind's  way 
of  perceiving  nature.  This  is  not   only  the  vaguely 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  43 

prevalent  theory,  but  is,  I  believe,  the  historical  form  of 
the  bifurcation  theory  in  so  far  as  it  is  derived  from 
philosophy.  I  shall  call  it  the  theory  of  psychic  additions. 

This  theory  of  psychic  additions  is  a  sound  common- 
sense  theory  which  lays  immense  stress  on  the  obvious 
reality  of  time,  space,  solidity  and  inertia,  but  distrusts 
the  minor  artistic  additions  of  colour,  warmth  and  sound. 

The  theory  is  the  outcome  of  common-sense  in 
retreat.  It  arose  in  an  epoch  when  the  transmission 
theories  of  science  were  being  elaborated.  For  example, 
colour  is  the  result  of  a  transmission  from  the  material 
object  to  the  perceiver's  eye;  and  what  is  thus  trans- 
mitted is  not  colour.  Thus  colour  is  not  part  of  the 
reality  of  the  material  object.  Similarly  for  the  same 
reason  sounds  evaporate  from  nature.  Also  warmth  is 
due  to  the  transfer  of  something  which  is  not  tempera- 
ture. Thus  we  are  left  with  spatio-temporal  positions, 
and  what  I  may  term  the  *  pushiness '  of  the  body.  This 
latias  us  to  eighteenth  and  nineteenth  century  material- 
ism, namely,  the  belief  that  what  is  real  in  nature  is 
matter,  in  time  and  in  space  and  with  inertia. 

Evidently  a  distinction  in  quality  has  been  presup- 
posed separating  off  some  perceptions  due  to  touch  from 
other  perceptions.  These  touch-perceptions  are  per- 
ceptions of  the  real  inertia,  whereas  the  other  perceptions 
are  psychic  additions  which  must  be  explained  on  the 
causal  theory.  This  distinction  is  the  product  of  an 
epoch  in  which  physical  science  has  got  ahead  of  medical 
pathology  and  of  physiology.  Perceptions  of  push  are 
just  as  much  the  outcome  of  transmission  as  are  per- 
ceptions of  colour.  When  colour  is  perceived  the  nerves 
of  the  body  are  excited  in  one  way  and  transmit  their 
message  towards  the  brain,  and  when  push  is  perceived 


44  THE  CONCEPT  OF  NATURE  [cH. 

other  nerves  of  the  body  are  excited  in  another  way  and 
transmit  their  message  towards  the  brain.  The  message 
of  the  one  set  is  not  the  conveyance  of  colour,  and  the 
message  of  the  other  set  is  not  the  conveyance  of  push. 
But  in  one  case  colour  is  perceived  and  in  the  other 
case  the  push  due  to  the  object.  If  you  snip  certain 
nerves,  there  is  an  end  to  the  perception  of  colour;  and 
if  you  snip  certain  other  nerves,  there  is  an  end  to  the 
perception  of  push.  It  would  appear  therefore  that  any 
reasons  which  should  remove  colour  from  the  reality  of 
nature  should  also  operate  to  remove  inertia. 

Thus  the  attempted  bifurcation  of  apparent  nature 
into  two  parts  of  which  one  part  is  both  causal  for  its 
own  appearance  and  for  the  appearance  of  the  other 
part,  which  is  purely  apparent,  fails  owing  to  the  failure 
to  establish  any  fundamental  distinction  between  our 
ways  of  knowing  about  the  two  parts  of  nature  as  thus 
partitioned.  I  am  not  denying  that  the  feeling  of 
muscular  effort  historically  led  to  the  formulation  of 
the  concept  of  force.  But  this  historical  fact  does  not 
warrant  us  in  assigning  a  superior  reality  in  nature  to 
material  inertia  over  colour  or  sound.  So  far  as  reality 
is  concerned  all  our  sense-perceptions  are  in  the  same 
boat,  and  must  be  treated  on  the  same  principle.  The 
evenness  of  treatment  is  exactly  what  this  compromise 
theory  fails  to  achieve. 

The  bifurcation  theory  however  dies  hard.  The 
reason  is  that  there  really  is  a  difficulty  to  be  faced  in 
relating  within  the  same  system  of  entities  the  redness 
of  the  fire  with  the  agitation  of  the  molecules.  In  another 
lecture  I  will  give  my  own  explanation  of  the  origin  of 
the  difficulty  and  of  its  solution. 

Another  favourite  solution,  the  most  attenuated  form 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  45 

which  the  bifurcation  theory  assumes,  is  to  maintain 
that  the  molecules  and  ether  of  science  are  purely 
conceptual.  Thus  there  is  but  one  nature,  namely 
apparent  nature,  and  atoms  and  ether  are  merely  names 
for  logical  terms  in  conceptual  formulae  of  calculation. 
But  what  is  a  formula  of  calculation }  It  is  presum- 
ably a  statement  that  something  or  other  is  true  for 
natural  occurrences.  Take  the  simplest  of  all  formulae, 
Two  and  two  make  four.  This — so  far  as  it  applies  to 
nature — asserts  that  if  you  take  two  natural  entities, 
and  then  again  two  other  natural  entities,  the  combined 
class  contains  four  natural  entities.  Such  formulae 
which  are  true  for  any  entities  cannot  result  in  the 
production  of  the  concepts  of  atoms.  Then  again  there 
are  formulae  which  assert  that  there  are  entities  in 
nature  with  such  and  such  special  properties,  say,  for 
example,  with  the  properties  of  the  atoms  of  hydrogen. 
Now  if  there  are  no  such  entities,  I  fail  to  see  how 
any  statements  about  them  can  apply  to  nature.  For 
example,  the  assertion  that  there  is  green  cheese  in  the 
moon  cannot  be  a  premiss  in  any  deduction  of  scientific 
importance,  unless  indeed  the  presence  of  green  cheese 
in  the  moon  has  been  verified  by  experiment.  The 
current  answer  to  these  objections  is  that,  though  atoms 
are  merely  conceptual,  yet  they  are  an  interesting  and 
picturesque  way  of  saying  something  else  which  is  true 
of  nature.  But  surely  if  it  is  something  else  that  you 
mean,  for  heaven's  sake  say  it.  Do  away  with  this 
elaborate  machinery  of  a  conceptual  nature  which 
consists  of  assertions  about  things  which  don't  exist  in 
order  to  convey  truths  about  things  which  do  exist. 
I  am  maintaining  the  obvious  position  that  scientific 
laws,  if  they  are  true,  are  statements  about  entities 


46  THE  CONCEPT  OF  NATURE  [ch. 

which  we  obtain  knowledge  of  as  being  in  nature ;  and 
that,  if  the  entities  to  which  the  statements  refer  are 
not  to  be  found  in  nature,  the  statements  about  them 
;  have  no  relevance  to  any  purely  natural  occurrence. 
I    Thus  the  molecules  and  electrons  of  scientific  theory 
i    are,  so  far  as  science  has  correctly  formulated  its  laws, 
;    each  of  them  factors  to  be  found  in  nature.  The  elec- 
trons are  only  hypothetical  in  so  far  as  we  are  not  quite 
certain  that  the  electron  theory  is  true.  But  their  hypo- 
thetical character  does  not  arise  from  the  essential  nature 
of  the  theory  in  itself  after  its  truth  has  been  granted. 
Thus  at  the  end  of  this  somewhat  complex  discussion, 
we  return  to  the  position  which  was  affirmed  at  its 
beginning.  The  primary  taslf^  of  a  philosophy  of  natural 
science  is  to  elucidate  the  concept  of  nature,  considered 
as  one  complex  fact  for  knowledge,  to  exhibit  the  funda- 
mental entities  and  the  fundamental  relations  between 
entities  in  terms  of  which  all  laws  of  nature  have  to  be 
stated,  and  to  secure  that  the  entities  and  relations  thus 
exhibited  are  adequate  for  the  expression  of  all  the 
relations  between  entities  which  occur  in  nature. 

The  third  requisite,  namely  that  of  adequacy,  is  the 
one  over  which  all  the  difficulty  occurs.  The  ultimate 
data  of  science  are  commonly  assumed  to  be  time,  space, 
material,  qualities  of  material,  and  relations  between 
material  objects.  But  data  as  they  occur  in  the  scientific 
laws  do  not  relate  all  the  entities  which  present  them- 
selves in  our  perception  of  nature.  For  example,  the 
wave-theory  of  light  is  an  excellent  well-established 
theory;  but  unfortunately  it  leaves  out  colour  as  per- 
ceived. Thus  the  perceived  redness — or,  other  colour — 
has  to  be  cut  out  of  nature  and  made  into  the  reaction 
of  the  mind  under  the  impulse  of  the  actual  events  of 


II]   THEORIES  OF  BIFURCATION  OF  NATURE  47 

nature.  In  other  words  this  concept  of  the  fundamental 
relations  within  nature  is  inadequate.  Thus  we  have 
to  bend  our  energies  to  the  enunciation  of  adequate 
concepts. 

But  in  so  doing,  are  we  not  in  fact  endeavouring  to 
solve  a  metaphysical  problem?  I  do  not  think  so.  We 
are  merely  endeavouring  to  exhibit  the  type  of  relations 
which  hold  between  the  entities  which  we.  in  fact  per- 
ceive as  in  nature.  We  are  not  called  on  to  make  any 
pronouncement  as  to  the  psychological  relation  of 
subjects  to  objects  or  as  to  the  status  of  either  in  the 
realm  of  reality.  It  is  true  that  the  issue  of  our  endeavour 
may  provide  material  which  is  relevant  evidence  for  a 
discussion  on  that  question.  It  can  hardly  fail  to  do  so. 
But  it  is  only  evidence,  and  is  not  itself  the  metaphysical 
discussion.  In  order  to  make  clear  the  character  of  this 
further  discussion  which  is  out  of  our  ken,  I  will  set 
before  you  two  quotations.  One  is  from  Schelling  and 
I  extract  the  quotation  from  the  work  of  the  Russian 
philosopher  Lossky  which  has  recently  been  so  ex- 
cellently translated  into  English  ^ — *  In  the  *' Philosophy 
of  Nature ''  I  considered  the  subject-object  called  nature 
in  its  activity  of  self-constructing.  In  order  to  under- 
stand it,  we  must  rise  to  an  intellectual  intuition  of  nature. 
The  empiricist  does  not  rise  thereto,  and  for  this  reason 
in  all  his  explanations  it  is  always  he  himself  that  proves 
to  be  constructing  nature.  It  is  no  wonder,  then,  that 
his  construction  and  that  which  was  to  be  constructed 
so  seldom  coincide.  A  Natur-philosoph  raises  nature  to 
independence,  and  makes  it  construct  itself,  and  he 
never  feels,  therefore,  the  necessity  of  opposing  nature 

1  The  Intuitive  Basis  of  Knowledge,  by  N.  O.  Lossky,  transl.  by 
Mrs  Duddington,  Macmillan  and  Co.,  19 19. 


48  THE  CONCEPT  OF  NATURE  [ch.  ii 

as  constructed  {i.e.  as  experience)  to  real  nature,  or  of 
correcting  the  one  by  means  of  the  other.' 

The  other  quotation  is  from  a  paper  read  by  the  Dean 
of  St  Paul's  before  the  Aristotelian  Society  in  May  of 
19 19.  Dr  Inge's  paper  is  entitled  *Platonism  and 
Human  Immortality,'  and  in  it  there  occurs  the  following 
statement:  *To  sum  up.  The  Platonic  doctrine  of  im- 
mortality rests  on  the  independence  of  the  spiritual  world. 
The  spiritual  world  is  not  a  world  of  unrealised  ideals, 
over  against  a  real  world  of  unspiritual  fact.  It  is,  on 
the  contrary,  the  real  world,  of  which  we  have  a  true 
though  very  incomplete  knowledge,  over  against  a  world 
of  common  experience  which,  as  a  complete  whole,  is 
not  real,  since  it  is  compacted  out  of  miscellaneous  data, 
not  all  on  the  same  level,  by  the  help  of  the  imagination. 
There  is  no  world  corresponding  to  the  world  of  our 
common  experience.  Nature  makes  abstractions  for  us, 
deciding  what  range  of  vibrations  we  are  to  see  and  hear, 
what  things  we  are  to  notice  and  remember.' 

I  have  cited  these  statements  because  both  of  them 
deal  with  topics  which,  though  they  lie  outside  the  range 
of  our  discussion,  are  always  being  confused  with  it. 
The  reason  is  that  they  lie  proximate  to  our  field  of 
thought,  and  are  topics  which  are  of  burning  interest 
to  the  metaphysically  minded.  It  is  difficult  for  a 
philosopher  to  realise  that  anyone  really  is  confining 
his  discussion  within  the  limits  that  I  have  set  before 
you.  The  boundary  is  set  up  just  where  he  is  beginning 
to  get  excited.  But  I  submit  to  you  that  among  the 
necessary  prolegomena  for  philosophy  and  for  natural 
science  is  a  thorough  understanding  of  the  types  of 
entities,  and  types  of  relations  among  those  entities, 
which  are  disclosed  to  us  in  our  perceptions  of  nature. 


CHAPTER  III 

TIME 

The  two  previous  lectures  of  this  course  have  been 
mainly  critical.  In  the  present  lecture  I  propose  to 
enter  upon  a  survey  of  the  kinds  of  entities  which  are 
posited  for  knowledge  in  sense-awareness.  My  purpose 
is  to  investigate  the  sorts  of  relations  which  these  entities 
of  various  kinds  can  bear  to  each  other.  A  classification 
of  natural  entities  is  the  beginning  of  natural  philosophy. 
To-day  we  commence  with  the  consideration  of  Time. 

In  the  first  place  there  is  posited  for  us  a  general 
fact:  namely,  something  is  going  on;  there  is  an  oc- 
currence for  definition. 

This  general  fact  at  once  yields  for  our  apprehension 
two  factors,  which  I  will  name,  the  *  discerned'  and  the 
*  discernible.'  The  discerned  is  comprised  of  those 
elements  of  the  general  fact  which  are  discriminated 
with  their  own  individual  peculiarities.  It  is  the  field 
directly  perceived.  But  the  entities  of  this  field  have 
relations  to  other  entities  which  are  not  particularly 
discriminated  in  this  individual  way.  These  other 
entities  are  known  merely  as  the  relata  in  relation  to  the 
entities  of  the  discerned  field.  Such  an  entity  is  merely 
a  *  something'  which  has  such-and-such  definite  rela- 
tions to  some  definite  entity  or  entities  in  the  discerned 
field.  As  being  thus  related,  they  are — owing  to  the 
particular  character  of  these  relations — ^known  as 
elements  of  the  general  fact  which  is  going  on.  But  we 
are  not  aware  of  them  except  as  entities  fulfilling  the 
functions  of  relata  in  these  relations. 

Thus  the  complete  general  fact,  posited  as  occurring, 
comprises  both  sets  of  entities,  namely  the  entities 


50  THE  CONCEPT  OF  NATURE  [ch. 

perceived  in  their  own  individuality  and  other  entities 
merely  apprehended  as  relata  without  further  definition. 
This  complete  general  fact  is  the  discernible  and  it 
comprises  the  discerned.  The  discernible  is  all  nature  as 
disclosed  in  that  sense-awareness,  and  extends  beyond 
and  comprises  all  of  nature  as  actually  discriminated 
or  discerned  in  that  sense-awareness.  The  discerning 
or  discrimination  of  nature  is  a  peculiar  awareness  of 
special  factors  in  nature  in  respect  to  their  peculiar  cha- 
racters. But  the  factors  in  nature  of  which  we  have  this 
peculiar  sense-awareness  are  known  as  not  comprising 
all  the  factors  which  together  form  the  whole  complex 
of  related  entities  within  the  general  fact  there  for 
discernment.  This  peculiarity  of  knowledge  is  what  I 
call  its  unexhaustive  character.  This  character  may  be 
metaphorically  described  by  the  statement  that  nature 
as  perceived  always  has  a  ragged  edge.  For  example, 
there  is  a  world  beyond  the  room  to  which  our  sight  is 
confined  known  to  us  as  completing  the  space-relations 
of  the  entities  discerned  within  the  room.  The  junction 
of  the  interior  world  of  the  room  with  the  exterior  world 
beyond  is  never  sharp.  Sounds  and  subtler  factors 
disclosed  in  sense-awareness  float  in  from  the  outside. 
Every  type  of  sense  has  its  own  set  of  discriminated 
entities  which  are  known  to  be  relata  in  relation  with 
entities  not  discriminated  by  that  sense.  For  example  we 
see  something  which  we  do  not  touch  and  we  touch 
something  which  we  do  not  see,  and  we  have  a  general 
sense  of  the  space-relations  between  the  entity  dis- 
closed in  sight  and  the  entity  disclosed  in  touch.  Thus 
in  the  first  place  each  of  these  two  entities  is  known  as 
a  relatum  in  a  general  system  of  space-relations  and 
in  the  second  place  the  particular  mutual  relation  of 


Ill]  TIME  51 

these  two  entities  as  related  to  each  other  in  this  general 
system  is  determined.  But  the  general  system  of  space- 
relations  relating  the  entity  discriminated  by  sight 
with  that  discriminated  by  sight  is  not  dependent  on 
the  peculiar  character  of  the  other  entity  as  reported 
by  the  alternative  sense.  For  example,  the  space- 
relations  of  the  thing  seen  would  have  necessitated  an 
entity  as  a  relatum  in  the  place  of  the  thing  touched 
even  although  certain  elements  of  its  character  had  not 
been  disclosed  by  touch.  Thus  apart  from  the  touch 
an  entity  with  a  certain  specific  relation  to  the  thing  seen 
would  have  been  disclosed  by  sense-awareness  but  not 
otherwise  discriminated  in  respect  to  its  individual 
character.  An  entity  merely  known  as  spatially  related 
to  some  discerned  entity  is  what  we  mean  by  the  bare 
idea  of  *  place.'  The  concept  of  place  marks  the  dis- 
closure in  sense-awareness  of  entities  in  nature  known 
merely  by  their  spatial  relations  to  discerned  entities. 
It  is  the  disclosure  of  the  discernible  by  means  of  its 
relations  to  the  discerned. 

This  disclosure  of  an  entity  as  a  relatum  without 
further  specific  discrimination  of  quality  is  the  basis  of 
our  concept  of  significance.  In  the  above  example  the 
thing  seen  was  significant,  in  that  it  disclosed  its  spatial 
relations  to  other  entities  not  necessarily  otherwise 
entering  into  consciousness.  Thus  significance  is  re- 
latedness,  but  it  is  relatedness  with  the  emphasis  on  one 
end  only  of  the  relation. 

For  the  sake  of  simplicity  I  have  confined  the  argu- 
ment to  spatial  relations;  but  the  same  considerations 
apply  to  temporal  relations.  The  concept  of  'period  of 
time '  marks  the  disclosure  in  sense-awareness  of  entities 
in  nature  known  merely  by  their  temporal  relations  to 

4—2 


52  THE  CONCEPT  OF  NATURE  [ch. 

discerned  entities.  Still  further,  this  separation  of  the 
ideas  of  space  and  time  has  merely  been  adopted  for  the 
sake  of  gaining  simplicity  of  exposition  by  conformity 
to  current  language.  What  we  discern  is  the  specific 
character  of  a  place  through  a  period  of  time.  This  is 
what  I  mean  by  an  *  event.'  We  discern  some  specific 
character  of  an  event.  But  in  discerning  an  event  we 
are  also  aware  of  its  significance  as  a  relatum  in  the  struc- 
ture of  events.  This  structure  of  events  is  the  complex 
of  events  as  related  by  the  two  relations  of  extension  and 
cogredience.  The  most  simple  expression  of  the  proper- 
ties of  this  structure  are  to  be  found  in  our  spatial  and 
temporal  relations.  A  discerned  event  is  known  as  related 
in  this  structure  to  other  events  whose  specific  characters 
are  otherwise  not  disclosed  in  that  immediate  awareness 
except  so  far  as  that  they  are  relata  within  the  structure. 
The  disclosure  in  sense-awareness  of  the  structure 
of  events  classifies  events  into  those  which  are  discerned 
in  respect  to  some  further  individual  character  and  those 
which  are  not  otherwise  disclosed  except  as  elements 
of  the  structure.  These  signified  events  must  include 
events  in  the  remote  past  as  well  as  events  in  the 
future.  We  are  aware  of  these  as  the  far  off  periods  of 
unbounded  time.  But  there  is  another  classification  of 
events  which  is  also  inherent  in  sense-awareness.  These 
are  the  events  which  share  the  immediacy  of  the  im- 
mediately present  discerned  events.  These  are  the  events 
whose  characters  together  with  those  of  the  discerned 
events  comprise  all  nature  present  for  discernment. 
They  form  the  complete  general  fact  which  is  all  nature 
now  present  as  disclosed  in  that  sense-awareness.  It  is 
in  this  second  classification  of  events  that  the  differentia- 
tion of  space  from  time  takes  its  origin.  The  germ  of 


Ill]  TIME  53 

space  is  to  be  found  in  the  mutual  relations  of  events 
within  the  immediate  general  fact  which  is  all  nature 
now  discernible,  namely  within  the  one  event  which  is 
the  totality  of  present  nature.  The  relations  of  other 
events  to  this  totality  of  nature  form  the  texture  of  time. 

The  unity  of  this  general  present  fact  is  expressed  by 
the  concept  of  simultaneity.  The  general  fact  is  the 
whole  simultaneous  occurrence  of  nature  which  is  now 
for  sense-awareness.  This  general  fact  is  what  I  have 
called  the  discernible.  But  in  future  I  will  call  it  a 
*  duration/  meaning  thereby  a  certain  whole  of  nature 
which  is  limited  only  by  the  property  of  being  a  simul- 
taneity. Further  in  obedience  to  the  principle  of  com- 
prising within  nature  the  whole  terminus  of  sense-aware- 
ness, simultaneity  must  not  be  conceived  as  an  irrelevant 
mental  concept  imposed  upon  nature.  Our  sense- 
awareness  posits  for  immediate  discernment  a  certain 
whole,  here  called  a  *  duration';  thus  a  duration  is  a 
definite  natural  entity.  A  duration  is  discriminated  as 
a  complex  of  partial  events,  and  the  natural  entities 
which  are  components  of  this  complex  are  thereby  said 
to  be  *  simultaneous  with  this  duration?  Also  in  a 
derivative  sense  they  are  simultaneous  with  each  other 
in  respect  to  this  duration.  Thus  simultaneity  is  a 
definite  natural  relation.  The  word  *  duration '  is  perhaps 
unfortunate  in  so  far  as  it  suggests  a  mere  abstract 
stretch  of  time.  This  is  not  what  I  mean.  A  duration  is 
a  concrete  slab  of  nature  limited  by  simultaneity  which 
is  an  essential  factor  disclosed  in  sense-awareness. 

Nature  is  a  process.  As  in  the  case  of  everything 
directly  exhibited  in  sense-awareness,  there  can  be  no 
explanation  of  this  characteristic  of  nature.  All  that 
can  be  done  is  to  use  language  which  may  speculatively 


54  THE  CONCEPT  OF  NATURE  [ch. 

demonstrate  it,  and  also  to  express  the  relation  of  this 
factor  in  nature  to  other  factors. 

It  is  an  exhibition  of  the  process  of  nature  that  each 
duration  happens  and  passes.  The  process  of  nature  can 
also  be  termed  the  passage  of  nature.  I  definitely  refrain 
at  this  stage  from  using  the  word  'time/  since  the 
measurable  time  of  science  and  of  civilised  life  generally 
merely  exhibits  some  aspects  of  the  more  fundamental 
fact  of  the  passage  of  nature.  I  believe  that  in  this 
doctrine  I  am  in  full  accord  with  Bergson,  though  he 
uses  *time'  for  the  fundamental  fact  which  I  call  the 
*  passage  of  nature.'  Also  the  passage  of  nature  is  ex- 
hibited equally  in  spatial  transition  as  well  as  in  temporal 
transition.  It  is  in  virtue  of  its  passage  that  nature  is 
always  moving  on.  It  is  involved  in  the  meaning  of  this 
property  of  *  moving  on '  that  not  only  is  any  act  of  sense- 
awareness  just  that  act  and  no  other,  but  the  terminus 
of  each  act  is  also  unique  and  is  the  terminus  of  no  other 
act.  Sense-awareness  seizes  its  only  chance  and  presents 
for  knowledge  something  which  is  for  it  alone. 

There  are  two  senses  in  which  the  terminus  of  sense- 
awareness  is  unique.  It  is  unique  for  the  sense-aware- 
ness of  an  individual  mind  and  it  is  unique  for  the 
sense-awareness  of  all  minds  which  are  operating  under 
natural  conditions.  There  is  an  important  distinction 
between  the  two  cases,  (i)  For  one  mind  not  only  is  the 
discerned  component  of  the  general  fact  exhibited  in 
any  act  of  sense-awareness  distinct  from  the  discerned 
component  of  the  general  fact  exhibited  in  any  other 
act  of  sense-awareness  of  that  mind,  but  the  two  corre- 
sponding durations  which  are  respectively  related  by 
simultaneity  to  the  two  discerned  components  are 
necessarily  distinct.  This  is  an  exhibition  of  the  temporal 


Ill]  TIME  55 

passage  of  nature ;  namely,  one  duration  has  passed  into 
the  other.  Thus  not  only  is  the  passage  of  nature  an 
essential  character  of  nature  in  its  rdle  of  the  terminus  of 
sense-awareness,   but   it   is   also   essential  for  sense- 
awareness  in  itself.   It  is  this  truth  which  makes  time 
appear  to  extend  beyond  nature.    But  what  extends 
beyond  nature  to  mind  is  not  the  serial  and  measurable 
time,  which  exhibits  merely  the  character  of  passage  in 
nature,  but  the  quality  of  passage  itself  which  is  in  no 
way  measurable  except  so  far  as  it  obtains  in  nature. 
That  is  to  say,  *  passage'  is  not  measurable  except  as 
it  occurs  in  nature  in  connexion  with  extension.    In 
passage  we  reach  a  connexion  of  nature  with  the  ultimate 
metaphysical  reality.  The  quality  of  passage  in  dura- 
tions is  a  particular  exhibition  in  nature  of  a  quality 
which  extends  beyond  nature.   For  example  passage  is 
a  quality  not  only  of  nature,  which  is  the  thing  known, 
but  also  of  sense-awareness  which  is  the  procedure  of 
knowing.  Durations  have  all  the  reality  that  nature  has," 
though  what  that  may  be  we  need  not  now  determine. 
The  measurableness  of  time  is  derivative  from  the 
properties  of  durations.    So  also  is  the  serial  character 
of  time.  We  shall  find  that  there  are  in  nature  competing 
serial  time-systems  derived  from  different  families  of 
durations.    These  are  a  peculiarity  of  the  character  of 
passage  as  it  is  found  in  nature.  This  character  has  the 
reality  of  nature,  but  we  must  not  necessarily  transfer 
natural  timeto  extra-natural  entities,  (ii)  Fortwo  minds, 
the  discerned  components  of  the  general  facts  exhibited 
in  their  respective  acts  of  sense-awareness  must  be 
different.   For  each  mind,  in  its  awareness  of  nature  is 
aware  of  a  certain  complex  of  related  natural  entities 
in  their  relations  to  the  living  body  as  a  focus.  But  the 


56  THE  CONCEPT  OF  NATURE  [ch. 

associated  durations  may  be  identical.  Here  we  are 
touching  on  that  character  of  the  passage  nature  which 
issues  in  the  spatial  relations  of  simultaneous  bodies. 
This  possible  identity  of  the  durations  in  the  case  of 
the  sense-awareness  of  distinct  minds  is  what  binds 
into  one  nature  the  private  experiences  of  sentient 
beings.  We  are  here  considering  the  spatial  side  of  the 
passage  of  nature.  Passage  in  this  aspect  of  it  also  seems 
to  extend  beyond  nature  to  mind. 

It  is  important  to  distinguish  simultaneity  from  in- 
stantaneousness.  I  lay  no  stress  on  the  mere  current 
usage  of  the  two  terms.  There  are  two  concepts  which 
I  want  to  distinguish,  and  one  I  call  simultaneity  and 
the  other  instantaneousness.  I  hope  that  the  words  are 
judiciously  chosen;  but  it  really  does  not  matter  so 
Jong  as  I  succeed  in  explaining  my  meaning.  Simul- 
Itaneity  is  the  property  of  a  group  of  natural  elements 
which  in  some  sense  are  components  of  a  duration. 
A  duration  can  be  all  nature  present  as  the  immediate 
fact  posited  by  sense-awareness.  A  duration  retains 
within  itself  the  passage  of  nature.  There  are  within  it 
antecedents  and  consequents  which  are  also  durations 
which  may  be  the  complete  specious  presents  of  quicker 
consciousnesses.  In  other  words  a  duration  retains 
temporal  thickness.  Any  concept  of  all  nature  as  imme- 
diately known  is  always  a  concept  of  some  duration 
though  it  may  be  enlarged  in  its  temporal  thickness 
beyond  the  possible  specious  present  of  any  being  known 
to  us  as  existing  within  nature.  Thus  simultaneity  is  an 
ultimate  factor  in  nature, immediate  for  sense-awareness. 

Instantaneousness  is  a  complex  logical  concept  of  a 
procedure  in  thought  by  which  constructed  logical 
entities  are  produced  for  the  sake  of  the  simple  ex- 


Ill]  TIME  57 

pression  in  thought  of  properties  of  nature.  Instan-I 
taneousness  is  the  concept  of  all  nature  at  an  instant, 
where  an  instant  is  conceived  as  deprived  of  all  tem- 
poral extension.  For  example  we  conceive  of  the  dis- 
tribution of  matter  in  space  at  an  instant.  This  is  a  very 
useful  concept  in  science  especially  in  applied  mathe- 
matics ;  but  it  is  a  very  complex  idea  so  far  as  concerns 
its  connexions  with  the  immediate  facts  of  sense- 
awareness.  There  is  no  such  thing  as  nature  at  an  instant 
posited  by  sense-awareness.  What  sense-awareness 
delivers  over  for  knowledge  is  nature  through  a  period. 
Accordingly  nature  at  an  instant,  since  it  is  not  itself 
a  natural  entity,  must  be  defined  in  terms  of  genuine 
natural  entities.  Unless  we  do  so,  our  science,  which 
employs  the  concept  of  instantaneous  nature,  must 
abandon  all  claim  to  be  founded  upon  observation. 

I  will  use  the  term  *  moment '  to  mean '  all  nature  at  an 
instant.'  A  moment,  in  the  sense  in  which  the  term  is 
here  used,  has  no  temporal  extension,  and  is  in  this  re- 
spect to  be  contrasted  with  a  duration  which  has  such 
extension.  What  is  directly  yielded  to  our  knowledge  by 
sense-awareness  is  a  duration.  Accordingly  we  have  now 
to  explain  how  moments  are  derived  from  durations,  and 
also  to  explain  the  purpose  served  by  their  introduction. 

A  moment  is  a  limit  to  which  we  approach  as  we 
confine  attention  to  durations  of  minimum  extension. 
Natural  relations  among  the  ingredients  of  a  duration 
gain  in  complexity  as  we  consider  durations  of  increasing 
temporal  extension.  Accordingly  there  is  an  approach 
to  ideal  simplicity  as  we  approach  an  ideal  diminution 
of  extension. 

The  word  Mimit'  has  a  precise  signification  in  the 
logic  of  number  and  even  in  the  logic  of  non-numerical 


58  THE  CONCEPT  OF  NATURE  [ch. 

one-dimensional  series.  As  used  here  it  is  so  far  a  mere 
metaphor,  and  it  is  necessary  to  explain  directly  the 
concept  which  it  is  meant  to  indicate. 

Durations  can  have  the  two-termed  relational  pro- 
perty of  extending  one  over  the  other.  Thus  the  duration 
which  is  all  nature  during  a  certain  minute  extends  over 
the  duration  which  is  all  nature  during  the  30th  second 
of  that  minute.  This  relation  of  'extending  over' — 
*  extension '  as  I  shall  call  it — is  a  fundamental  natural 
relation  whose  field  comprises  more  than  durations.  It 
is  a  relation  which  two  limited  events  can  have  to  each 
other.  Furthermore  as  holding  between  durations  the 
relation  appears  to  refer  to  the  purely  temporal  ex- 
tension. I  shall  however  maintain  that  the  same  relation 
of  extension  lies  at  the  base  both  of  temporal  and  spatial 
extension.  This  discussion  can  be  postponed;  and  for 
the  present  we  are  simply  concerned  with  the  relation 
of  extension  as  it  occurs  in  its  temporal  aspect  for  the 
limited  field  of  durations. 

The  concept  of  extension  exhibits  in  thought  one  side 
of  the  ultimate  passage  of  nature.  This  relation  holds 
because  of  the  special  character  which  passage  assumes 
in  nature ;  it  is  the  relation  which  in  the  case  of  durations 
expresses  the  properties  of  'passing  over.'  Thus  the 
duration  which  was  one  definite  minute  passed  over  the 
duration  which  was  its  30th  second.  The  duration  of  the 
30th  second  was  part  of  the  duration  of  the  minute.  I  shall 
use  the  terms  *  whole  'and '  part '  exclusively  in  this  sense, 
that  the  *  part '  is  an  event  which  is  extended  over  by  the 
other  event  which  is  the  '  whole.'  Thus  in  my  nomencla- 
ture '  whole '  and  '  part '  refer  exclusively  to  this  funda- 
mental relation  of  extension;  and  accordingly  in  this 
technical  usage  only  events  can  be  either  wholes  or  parts. 


Ill]  TIME  59 

The  continuity  of  nature  arises  from  extension.  Every  I 
event  extends  over  other  events,  and  every  event  is  I 
extended  over  by  other  events.  Thus  in  the  special  case  of 
durations  which  are  now  the  only  events  directly  under 
consideration,  every  duration  is  part  of  other  durations ; 
and   every   duration   has   other   durations   which   are 
parts  of  it.   Accordingly  there  are  no  maximum  dura-  ) 
tions  and  no  minimum  durations.    Thus  there  is  no/ 
atomic  structure  of  durations,  and  the  perfect  definition  \ 
of  a  duration,  so  as  to  mark  out  its  individuality  and 
distinguish  it  from  highly  analogous  durations  over 
which  it  is  passing,  or  which  are  passing  over  it,  is  an 
arbitrary  postulate  of  thought.   Sense-awareness  posits 
durations  as  factors  in  nature  but  does  not  clearly  enable 
thought  to  use  it  as  distinguishing  the  separate  indi- 
vidualities of  the  entities  of  an  allied  group  of  slightly 
differing  durations.  This  is  one  instance  of  the  in- 
determinateness  of  sense-awareness.    Exactness  is  an 
ideal  of  thought,  and  is  only  realised  in  experience  by 
the  selection  of  a  route  of  approximation. 

The  absence  of  maximum  and  minimum  durations 
does  not  exhaust  the  properties  of  nature  which  make 
up  its  continuity.  The  passage  of  nature  involves  the 
existence  of  a  family  of  durations.  When  two  durations 
belong  to  the  same  family  either  one  contains  the  other, 
or  they  overlap  each  other  in  a  subordinate  duration 
without  either  containing  the  other;  or  they  are  com- 
pletely separate.  The  excluded  case  is  that  of  durations 
overlapping  in  finite  events  but  not  containing  a  third 
duration  as  a  common  part. 

It  is  evident  that  the  relation  of  extension  is  transitive ; 
namely  as  applied  to  durations,  if  duration  A  is  part  of 
duration  B,  and  duration  B  is  part  of  duration  C,  then  A 


6o  THE  CONCEPT  OF  NATURE  [ch. 

is  part  of  C.  Thus  the  first  two  cases  may  be  combined 
into  one  and  we  can  say  that  two  durations  which 
belong  to  the  same  family  either  are  such  that  there  are 
durations  which  are  parts  of  both  or  are  completely 
separate. 

Furthermore  the  converse  of  this  proposition  holds ; 
namely,  if  two  durations  have  other  durations  which  are 
parts  of  both  or  if  the  two  durations  are  completely 
separate,  then  they  belong  to  the  same  family. 

The  further  characteristics  of  the  continuity  of 
nature — so  far  as  durations  are  concerned — which  has 
not  yet  been  formulated  arises  in  connexion  with'  a 
family  of  durations.  It  can  be  stated  in  this  way :  There 
are  durations  which  contain  as  parts  any  two  durations 
of  the  same  family.  For  example  a  week  contains  as 
parts  any  two  of  its  days.  It  is  evident  that  a  containing 
duration  satisfies  the  conditions  for  belonging  to  the 
same  family  as  the  two  contained  durations. 

We  are  now  prepared  to  proceed  to  the  definition  of 
a  moment  of  time.  Consider  a  set  of  durations  all  taken 
from  the  same  family.  Let  it  have  the  following  pro- 
perties :  (i)  of  any  two  members  of  the  set  one  contains 
the  other  as  a  part,  and  (ii)  there  is  no  duration  which 
is  a  common  part  of  every  member  of  the  set. 

Now  the  relation  of  whole  and  part  is  asymmetrical ; 
and  by  this  I  mean  that  if  A  is  part  of  B,  then  B  is  not 
part  of  A,  Also  we  have  already  noted  that  the  relation 
is  transitive.  Accordingly  we  can  easily  see  that  the 
durations  of  any  set  with  the  properties  just  enumerated 
must  be  arranged  in  a  one-dimensional  serial  order  in 
which  as  we  descend  the  series  we  progressively  reach 
durations  of  smaller  and  smaller  temporal  extension. 
The  series  may  start  with  any  arbitrarily  assumed 


Ill]  TIME  6i 

duration  of  any  temporal  extension,  but  in  descending 
the  series  the  temporal  extension  progressively  con- 
tracts and  the  successive  durations  are  packed  one  within 
the  other  like  the  nest  of  boxes  of  a  Chinese  toy.  But 
the  set  differs  from  the  toy  in  this  particular:  the  toy 
has  a  smallest  box  which  forms  the  end  box  of  its  series ; 
but  the  set  of  durations  can  have  no  smallest  duration 
nor  can  it  converge  towards  a  duration  as  its  limit.  For 
the  parts  either  of  the  end  duration  or  of  the  limit  would 
be  parts  of  all  the  durations  of  the  set  and  thus  the 
second  condition  for  the  set  would  be  violated. 

I  will  call  such  a  set  of  durations  an  *  abstractive  set ' 
of  durations.  It  is  evident  that  an  abstractive  set  as  we 
pass  along  it  converges  to  the  ideal  of  all  nature  with 
no  temporal  extension,  namely,  to  the  ideal  of  all  nature 
at  an  instant.  But  this  ideal  is  in  fact  the  ideal  of  a 
nonentity.  What  the  abstractive  set  is  in  fact  doing  is 
to  guide  thought  to  the  consideration  of  the  progressive 
simplicity  of  natural  relations  as  we  progressively 
diminish  the  temporal  extension  of  the  duration  con- 
sidered. Now  the  whole  point  of  the  procedure  is  that 
the  quantitative  expressions  of  these  natural  properties 
do  converge  to  limits  though  the  abstractive  set  does 
not  converge  to  any  limiting  duration.  The  laws  relating 
these  quantitative  limits  are  the  laws  of  nature  *  at  an 
instant,'  although  in  truth  there  is  no  nature  at  an 
instant  and  there  is  only  the  abstractive  set.  Thus  an 
abstractive  set  is  effectively  the  entity  meant  when  we 
consider  an  instant  of  time  without  temporal  extension. 
It  subserves  all  the  necessary  purposes  of  giving  a 
definite  meaning  to  the  concept  of  the  properties  of 
nature  at  an  instant.  I  fully  agree  that  this  concept  is 
fundamental  in  the  expression  of  physical  science.  The 


62  THE  CONCEPT  OF  NATURE  [ch. 

difficulty  is  to  express  our  meaning  in  terms  of  the  imme- 
diate deliverances  of  sense-awareness,  and  I  offer  the 
above  explanation  as  a  complete  solution  of  the  problem. 

In  this  explanation  a  moment  is  the  set  of  natural 
properties  reached  by  a  route  of  approximation.  An 
abstractive  series  is  a  route  of  approximation.  There  are 
different  routes  of  approximation  to  the  same  limiting 
set  of  the  properties  of  nature.  In  other  words  there 
are  different  abstractive  sets  which  are  to  be  regarded 
as  routes  of  approximation  to  the  same  moment. 
Accordingly  there  is  a  certain  amount  of  technical  detail 
necessary  in  explaining  the  relations  of  such  abstractive 
sets  with  the  same  convergence  and  in  guarding  against 
possible  exceptional  cases.  Such  details  are  not  suitable 
for  exposition  in  these  lectures,  and  I  have  dealt  with 
them  fully  elsewhere^. 

It  is  more  convenient  for  technical  purposes  to  look 
on  a  moment  as  being  the  class  of  all  abstractive  sets  of 
durations  with  the  same  convergence.  With  this  defini- 
tion (provided  that  we  can  successfully  explain  what 
we  mean  by  the  *same  convergence'  apart  from  a 
detailed  knowledge  of  the  set  of  natural  properties 
arrived  at  by  approximation)  a  moment  is  merely  a  class 
of  sets  of  durations  whose  relations  of  extension  in 
respect  to  each  other  have  certain  definite  peculiarities. 
We  may  term  these  connexions  of  the  component 
durations  the  *  extrinsic'  properties  of  a  moment;  the 
*  intrinsic '  properties  of  the  moment  are  the  properties 
of  nature  arrived  at  as  a  limit  as  we  proceed  along  any 
one  of  its  abstractive  sets.  These  are  the  properties  of 
nature  *at  that  moment,'  or  *at  that  instant.' 

^  Cf .  An  Enquiry  concerning  the  Principles  of  Natural  Knowledge^ 
Cambridge  University  Press,  19 19. 


Ill]  •  TIME  63 

The  durations  which  enter  into  the  composition  of 
a  moment  all  belong  to  one  family.  Thus  there  is  one 
family  of  moments  corresponding  to  one  family  of 
durations.  Also  if  we  take  two  moments  of  the  same 
family,  among  the  durations  which  enter  into  the  com- 
position of  one  moment  the  smaller  durations  are 
completely  separated  from  the  smaller  durations  which 
enter  into  the  composition  of  the  other  moment.  Thus 
the  two  moments  in  their  intrinsic  properties  must 
exhibit  the  limits  of  completely  different  states  of  nature. 
In  this  sense  the  two  moments  are  completely  separated. 
I  will  call  two  moments  of  the  same  family  *  parallel.' 

Corresponding  to  each  duration  there  are  two 
moments  of  the  associated  family  of  moments  which 
are  the  boundary  moments  of  that  duration.  A 
*  boundary  moment'  of  a  duration  can  be  defined  in 
this  way.  There  are  durations  of  the  same  family  as  the 
given  duration  which  overlap  it  but  are  not  contained 
in  it.  Consider  an  abstractive  set  of  such  durations. 
Such  a  set  defines  a  moment  which  is  just  as  much 
without  the  duration  as  within  it.  Such  a  moment  is  a 
boundary  moment  of  the  duration.  Also  we  call  upon 
our  sense-awareness  of  the  passage  of  nature  to  inform 
us  that  there  are  two  such  boundary  moments,  namely 
the  earlier  one  and  the  later  one.  We  will  call  them  the 
initial  and  the  final  boundaries. 

There  are  also  moments  of  the  same  family  such  that 
the  shorter  durations  in  their  composition  are  entirely 
separated  from  the  given  duration.  Such  moments  will 
be  said  to  lie  *  outside'  the  given  duration.  Again  other 
moments  of  the  family  are  such  that  the  shorter  dura- 
tions in  their  composition  are  parts  of  the  given  dura- 
tion.   Such  moments  are  said  to  lie  *  within'  the  given 


64  THE  CONCEPT  OF  NATURE  [ch. 

duration  or  to  *  inhere '  in  it.  The  whole  family  of  parallel 
moments  is  accounted  for  in  this  way  by  reference  to 
any  given  duration  of  the  associated  family  of  durations. 
Namely,  there  are  moments  of  the  family  which  lie 
without  the  given  duration,  there  are  the  two  moments 
which  are  the  boundary  moments  of  the  given  duration, 
and  the  moments  which  lie  within  the  given  duration. 
Furthermore  any  two  moments  of  the  same  family  are 
the  boundary  moments  of  some  one  duration  of  the 
associated  family  of  durations. 

It  is  now  possible  to  define  the  serial  relation  of 
temporal  order  among  the  moments  of  a  family.  For 
let  A  and  C  be  any  two  moments  of  the  family,  these 
moments  are  the  boundary  moments  of  one  duration  d 
of  the  associated  family,  and  any  moment  B  which  lies 
within  the  duration  d  will  be  said  to  lie  between  the 
moments  A  and  C.  Thus  the  three-termed  relation  of 
*  lying-between '  as  relating  three  moments  A,  B,  and  C 
is  completely  defined .  Also  our  knowledge  of  the  passage 
of  nature  assures  us  that  this  relation  distributes  the 
moments  of  the  family  into  a  serial  order.  I  abstain 
from  enumerating  the  definite  properties  which  secure 
this  result,  I  have  enumerated  them  in  my  recently 
published  book^  to  which  I  have  already  referred. 
Furthermore  the  passage  of  nature  enables  us  to  know 
that  one  direction  along  the  series  corresponds  to 
passage  into  the  future  and  the  other  direction  corre- 
sponds to  retrogression  towards  the  past. 

Such  an  ordered  series  of  moments  is  what  we  mean 
by  time  defined  as  a  series.  Each  element  of  the  series 
exhibits  an  instantaneous  state  of  nature.  Evidently  this 
serial  time  is  the  result  of  an  intellectual  process  of 

1  CL  Enquiry, 


Ill]  TIME  65 

abstraction.  What  I  have  done  is  to  give  precise  defini- 
tions of  the  procedure  by  which  the  abstraction  is 
effected.  This  procedure  is  merely  a  particular  case  of 
the  general  method  which  in  my  book  I  name  the 
*  method  of  extensive  abstraction.'  This  serial  time  is 
evidently  not  the  very  passage  of  nature  itself.  It 
exhibits  some  of  the  natural  properties  which  flow  from 
it.  The  state  of  nature  *  at  a  moment '  has  evidently  lost 
this  ultimate  quality  of  passage.  Also  the  temporal 
series  of  moments  only  retains  it  as  an  extrinsic  relation 
of  entities  and  not  as  the  outcome  of  the  essential  being 
of  the  terms  of  the  series. 

Nothing  has  yet  been  said  as  to  the  measurement  of 
time.  Such  measurement  does  not  follow  from  the 
mere  serial  property  of  time;  it  requires  a  theory  of 
congruence  which  will  be  considered  in  a  later  lecture. 

In  estimating  the  adequacy  of  this  definition  of  the 
temporal  series  as  a  formulation  of  experience  it  is 
necessary  to  discriminate  between  the  crude  deliverance 
of  sense-awareness  and  our  intellectual  theories.  The 
lapse  of  time  is  a  measurable  serial  quantity.  The  whole 
of  scientific  theory  depends  on  this  assumption  and  any 
theory  of  time  which  fails  to  provide  such  a  measurable 
series  stands  self-condemned  as  unable  to  account  for 
the  most  salient  fact  in  experience.  Our  difficulties  only 
begin  when  we  ask  what  it  is  that  is  measured.  It  is 
evidently  something  so  fundamental  in  experience  that 
we  can  hardly  stand  back  from  it  and  hold  it  apart  so 
as  to  view  it  in  its  own  proportions. 

We  have  first  to  make  up  our  minds  whether  time  is 
to  be  found  in  nature  or  nature  is  to  be  found  in  time. 
The  difficulty  of  the  latter  alternative — namely  of 
making  time  prior  to  nature — is  that  time  then  becomes 


66  THE  CONCEPT  OF  NATURE  [ch. 

a  metaphysical  enigma.  What  sort  of  entities  are  its 
instants  or  its  periods  ?  The  dissociation  of  time  from 
events  discloses  to  our  immediate  inspection  that  the 
attempt  to  set  up  time  as  an  independent  terminus  for 
knowledge  is  like  the  effort  to  find  substance  in  a  shadow. 
a-  [Fhere  is  time  because  there  are  happenings,  and  apart 
r  ^/    jfrom  happenings  there  is  nothing. 

It  is  necessary  however  to  make  a  distinction.  In 
some  sense  time  extends  beyond  nature.  It  is  not  true 
that  a  timeiess  sense-awareness  and  a  timeless  thought 
combine  to  contemplate  a  timeful  nature.  Sense-aware- 
ness and  thought  are  themselves  processes  as  well  as 
their  termini  in  nature.  In  other  words  there  is  a 
passage  of  sense-awareness  and  a  passage  of  thought. 
Thus  the  reign  of  the  quality  of  passage  extends  beyond 
nature.  But  now  the  distinction  arises  between  passage 
which  is  fundamental  and  the  temporal  series  which  is 
a  logical  abstraction  representing  some  of  the  properties 
of  nature.  A  temporal  series,  as  we  have  defined  it, 
represents  merely  certain  properties  of  a  family  of 
durations — properties  indeed  which  durations  only 
possess  because  of  their  partaking  of  the  character  of 
passage,  but  on  the  other  hand  properties  which  only 
durations  do  possess.  Accordingly  time  in  the  sense  of  a 
measurable  temporal  series  is  a  character  of  nature  only, 
and  does  not  extend  to  the  processes  of  thought  and  of 
sense-awareness  except  by  a  correlation  of  these  processes 
with  the  temporal  series  implicated  in  their  procedures. 

So  far  the  passage  of  nature  has  been  considered  in 
connexion  with  the  passage  of  durations;  and  in  this 
connexion  it  is  peculiarly  associated  with  temporal 
series.  We  must  remember  however  that  the  character 
of  passage  is  peculiarly  associated  with  the  extension  of 


Ill]  TIME  67 

events,  and  that  from  this  extension  spatial  transition 
arises  just  as  much  as  temporal  transition.  The  dis- 
cussion of  this  point  is  reserved  for  a  later  lecture  but 
it  is  necessary  to  remember  it  now  that  we  are  pro- 
ceeding to  discuss  the  application  of  the  concept  of 
passage  beyond  nature,  otherwise  we  shall  have  too 
narrow  an  idea  of  the  essence  of  passage. 

It  is  necessary  to  dwell  on  the  subject  of  sense-aware- 
ness in  this  connexion  as  an  example  of  the  way  in 
which  time  concerns  mind,  although  measurable  time  is 
a  mere  abstract  from  nature  and  nature  is  closed  to  mind. 

Consider  sense-awareness — ^not  its  terminus  which 
is  nature,  but  sense-awareness  in  itself  as  a  procedure 
of  mind.  Sense-awareness  is  a  relation  of  mind  to 
nature.  Accordingly  we  are  now  considering  mind  as 
a  relatum  in  sense-awareness.  For  mind  there  is  the 
immediate  sense-awareness  and  there  is  memory.  The 
distinction  between  memory  and  the  present  immediacy 
has  a  double  bearing.  On  the  one  hand  it  discloses  that 
mind  is  not  impartially  aware  of  all  those  natural 
durations  to  which  it  is  related  by  awareness.  Its 
awareness  shares  in  the  passage  of  nature.  We  can 
imagine  a  being  whose  awareness,  conceived  as  his 
private  possession,  suffers  no  transition,  although  the 
terminus  of  his  awareness  is  our  own  transient  nature. 
There  is  no  essential  reason  why  memory  should  not 
be  raised  to  the  vividness  of  the  present  fact ;  and  then 
from  the  side  of  mind.  What  is  the  difference  between 
the  present  and  the  past?  Yet  with  this  hypothesis  we 
can  also  suppose  that  the  vivid  remembrance  and  the 
present  fact  are  posited  in  awareness  as  in  their  temporal 
serial  order.  Accordingly  we  must  admit  that  though 
we  can  imagine  that  mind  in  the  operation  of  sense- 

5—2 


68  THE  CONCEPT  OF  NATURE  [ch. 

awareness  might  be  free  from  any  character  of  passage, 
yet  in  point  of  fact  our  experience  of  sense-awareness 
exhibits  our  minds  as  partaking  in  this  character. 

On  the  other  hand  the  mere  fact  of  memory  is  an 
escape  from  transience.  In  memory  the  past  is  present. 
It  is  not  present  as  overleaping  the  temporal  succession 
of  nature,  but  it  is  present  as  an  immediate  fact  for 
the  mind.  Accordingly  memory  is  a  disengagement  of 
the  mind  from  the  mere  passage  of  nature ;  for  what  has 
passed  for  nature  has  not  passed  for  mind. 

Furthermore  the  distinction  between  memory  and 
the  immediate  present  is  not  so  clear  as  it  is  conventional 
to  suppose.  There  is  an  intellectual  theory  of  time  as  a 
moving  knife-edge,  exhibiting  a  present  fact  without 
temporal  extension.  This  theory  arises  from  the  concept 
of  an  ideal  exactitude  of  observation.  Astronomical 
observations  are  successively  refined  to  be  exact  to 
tenths,  to  hundredths,  and  to  thousandths  of  seconds. 
But  the  final  refinements  are  arrived  at  by  a  system  of 
averaging,  and  even  then  present  us  with  a  stretch  of 
time  as  a  margin  of  error.  Here  error  is  merely  a  con- 
ventional term  to  express  the  fact  that  the  character  of 
experience  does  not  accord  with  the  ideal  of  thought. 
I  have  already  explained  how  the  concept  of  a  moment 
conciliates  the  observed  fact  with  this  ideal;  namely, 
there  is  a  limiting  simplicity  in  the  quantitative  ex- 
pression of  the  properties  of  durations,  which  is 
arrived  at  by  considering  any  one  of  the  abstractive 
sets  included  in  the  moment.  In  other  words  the 
extrinsic  character  of  the  moment  as  an  aggregate  of 
durations  has  associated  with  it  the  intrinsic  character 
of  the  moment  which  is  the  limiting  expression  of 
natural  properties. 


Ill]  TIME  69 

Thus  the  character  of  a  moment  and  the  ideal  of 
exactness  which  it  enshrines  do  not  in  any  way  weaken 
the  position  that  the  ultimate  terminus  of  awareness  is 
a  duration  with  temporal  thickness.  This  immediate 
duration  is  not  clearly  marked  out  for  our  apprehension. 
Its  earlier  boundary  is  blurred  by  a  fading  into  memory, 
and  its  later  boundary  is  blurred  by  an  emergence  from 
anticipation.  There  is  no  sharp  distinction  either  between 
memory  and  the  present  immediacy  or  between  the 
present  immediacy  and  anticipation.  The  present  is  a 
wavering  breadth  of  boundary  between  the  two  ex-  ; 
tremes.  Thus  our  own  sense-awareness  with  its  extended 
present  has  some  of  the  character  of  the  sense-awareness 
of  the  imaginary  being  whose  mind  was  free  from  passage 
and  who  contemplated  all  nature  as  an  immediate  fact. 
Our  own  present  has  its  antecedents  and  its  consequents, 
and  for  the  imaginary  being  all  nature  has  its  ante- 
cedent and  its  consequent  durations.  Thus  the  only 
difference  in  this  respect  between  us  and  the  imaginary 
being  is  that  for  him  all  nature  shares  in  the  immediacy 
of  our  present  duration. 

The  conclusion  of  this  discussion  is  that  so  far  as 
sense-awareness  is  concerned  there  is  a  passage  of 
mind  which  is  distinguishable  from  the  passage  of 
nature  though  closely  allied  with  it.  We  may  speculate, 
if  we  like,  that  this  alliance  of  the  passage  of  mind  with 
the  passage  of  nature  arises  from  their  both  sharing  in 
some  ultimate  character  of  passage  which  dominates 
all  being.  But  this  is  a  speculation  in  which  we  have 
no  concern.  The  immediate  deduction  which  is  suffi- 
cient for  us  is  that — so  far  as  sense-awareness  is  con- 
cerned— mind  is  not  in  time  or  in  space  in  the  same 
sense  in  which  the  events  of  nature  are  in  time,  but 


!i 


y 


70  THE  CONCEPT  OF  NATURE  [ch. 

that  it  is  derivatively  in  time  and  in  space  by  reason  of 
the  peculiar  alliance  of  its  passage  with  the  passage 
of  nature.  Thus  mind  is  in  time  and  in  space  in  a  sense 
peculiar  to  itself.  This  has  been  a  long  discussion  to 
arrive  at  a  very  simple  and  obvious  conclusion.  We  all 
feel  that  in  some  sense  our  minds  are  here  in  this  room 
and  at  this  time.  But  it  is  not  quite  in  the  same  sense 
as  that  in  which  the  events  of  nature  which  are  the 
existences  of  our  brains  have  their  spatial  and  temporal 
positions.  The  fundamental  distinction  to  remember  is 
that  immediacy  for  sense-awareness  is  not  the  same  as 
instantaneousness  for  nature.  This  last  conclusion  bears 
on  the  next  discussion  with  which  I  will  terminate  this 
lecture.  This  question  can  be  formulated  thus,  Can 
alternative  temporal  series  be  found  in  nature  .f^ 

A  few  years  ago  such  a  suggestion  would  have  been 
put  aside  as  being  fantastically  impossible .  It  would  have 
had  no  bearing  on  the  science  then  current,  and  was 
akin  to  no  ideas  which  had  ever  entered  into  the  dreams 
of  philosophy.  The  eighteenth  and  nineteenth  centuries 
accepted  as  their  natural  philosophy  a  certain  circle  of 
concepts  which  were  as  rigid  and  definite  as  those  of 
the  philosophy  of  the  middle  ages,  and  were  accepted 
with  as  little  critical  research.  I  will  call  this  natural 
philosophy  *  materialism.'  Not  only  were  men  of  science 
materialists,  but  also  adherents  of  all  schools  of  philo- 
sophy. The  idealists  only  differed  from  the  philosophic 
materialists  on  question  of  the  alignment  of  nature  in 
reference  to  mind.  But  no  one  had  any  doubt  that  the 
philosophy  of  nature  considered  in  itself  was  of  the 
type  which  I  have  called  materialism.  It  is  the  philo- 
sophy which  I  have  already  examined  in  my  two 
lectures  of  this  course  preceding  the  present  one.    It 


Ill]  TIME  71 

can  be  summarised  as  the  belief  that  nature  is  an  aggre- 
gate of  material  and  that  this  material  exists  in  some 
sense  at  each  successive  member  of  a  one-dimensional 
series  of  extensionless  instants  of  time.  Furthermore 
the  mutual  relations  of  the  material  entities  at  each 
instant  formed  these  entities  into  a  spatial  configuration 
in  an  unbounded  space.  It  would  seem  that  space — on 
this  theory — ^would  be  as  instantaneous  as  the  instants, 
and  that  some  explanation  is  required  of  the  relations 
between  the  successive  instantaneous  spaces.  The 
materialistic  theory  is  however  silent  on  this  point; 
and  the  succession  of  instantaneous  spaces  is  tacitly 
combined  into  one  persistent  space.  This  theory  is  a 
purely  intellectual  rendering  of  experience  which  has 
had  the  luck  to  get  itself  formulated  at  the  dawn  of 
scientific  thought.  It  has  dominated  the  language  and 
the  imagination  of  science  since  science  flourished  in 
Alexandria,  with  the  result  that  it  is  now  hardly  possible 
to  speak  without  appearing  to  assume  its  immediate 
obviousness. 

But  when  it  is  distinctly  formulated  in  the  abstract 
terms  in  which  I  have  just  stated  it,  the  theory  is  very 
far  from  obvious.  The  passing  complex  of  factors  which 
compose  the  fact  which  is  the  terminus  of  sense-aware- 
ness places  before  us  nothing^  corresponding  to  the 
trinity  of  this  natural  materialism.  This  trinity  is  com- 
posed (i)  of  the  temporal  series  of  extensionless  instants, 
(ii)  of  the  aggregate  of  material  entities,  and  (iii)  of 
space  which  is  the  outcome  of  relations  of  matter. 

There  is  a  wide  gap  between  these  presuppositions 
of  the  intellectual  theory  of  materialism  and  the  im- 
mediate deliverances  of  sense-awareness.  I  do  not 
question  that  this  materialistic  trinity  embodies  im- 


72  THE  CONCEPT  OF  NATURE  [ch. 

portant  characters  of  nature.    But  it  is  necessary  to 
express    these    characters    in   terms   of  the   facts   of 
experience.  This  is  exactly  what  in  this  lecture  I  have 
been  endeavouring  to  do  so  far  as  time  is  concerned; 
and  we  have  now  come  up  against  the  question,  Is 
there  only  one  temporal  series  ?  The  uniqueness  of  the 
temporal    series    is    presupposed    in    the    materialist 
philosophy  of  nature.   But  that  philosophy  is  merely  a 
theory,  like  the  Aristotelian  scientific  theories  so  firmly 
believed  in  the  middle  ages.    If  in  this  lecture  I  have 
in  any  way  succeeded  in  getting  behind  the  theory  to 
the  immediate  facts,  the  answer  is  not  nearly  so  certain. 
The  question  can  be  transformed  into  this  alternative 
form.  Is  there  only  one  family  of  durations?    In  this 
question  the  meaning  of  a  *  family  of  durations'  has 
been  defined  earlier  in  this  lecture.  The  answer  is  now 
not  at  all  obvious.    On  the  materialistic  theory  the 
instantaneous  present  is  the  only  field  for  the  creative 
activity  of  nature.  The  past  is  gone  and  the  future  is 
not  yet.  Thus  (on  this  theory)  the  immediacy  of  per- 
ception is  of  an  instantaneous  present,  and  this  unique 
present  is  the  outcome  of  the  past  and  the  promise  of 
the  future.    But  we  deny  this  immediately  given  in- 
stantaneous present.  There  is  no  such  thing  to  be  found 
iin  nature.  As  an  ultimate  fact  it  is  a  nonentity.  What 
is  immediate  for  sense-awareness  is  a  duration.  Now  a 
duration  has  within  itself  a  past  and  a  future ;  and  the 
temporal  breadths  of  the  immediate  durations  of  sense- 
awareness  are  very  indeterminate  and  dependent  on  the 
individual  percipient.   Accordingly  there  is  no  unique 
factor  in  nature  which  for  every  percipient  is  pre- 
eminently and  necessarily  the  present.  The  passage  of 
nature  leaves  nothing  between  the  past  and  the  future. 


Ill]  TIME  73 

What  we  perceive  as  present  is  the  vivid  fringe  of 
memory  tinged  with  anticipation.  This  vividness  Hghts 
up  the  discriminated  field  within  a  duration.  But  no 
assurance  can  thereby  be  given  that  the  happenings  of 
nature  cannot  be  assorted  into  other  durations  of  aker- 
native  famiHes.  We  cannot  even  know  that  the  series 
of  immediate  durations  posited  by  the  sense-awareness 
of  one  individual  mind  all  necessarily  belong  to  the 
same  family  of  durations.  There  is  not  the  slightest 
reason  to  believe  that  this  is  so.  Indeed  if  my  theory  of 
nature  be  correct,  it  will  not  be  the  case. 

The  materialistic  theory  has  all  the  completeness  of 
the  thought  of  the  middle  ages,  which  had  a  complete 
answer  to  everything,  be  it  in  heaven  or  in  hell  or  in 
nature.  There  is  a  trimness  about  it,  with  its  instan- 
taneous present,  its  vanished  past,  its  non-existent 
future,  and  its  inert  matter.  This  trimness  is  very 
medieval  and  ill  accords  with  brute  fact. 

The  theory  which  I  am  urging  admits  a  greater 
ultimate  mystery  and  a  deeper  ignorance.  The  past  and 
the  future  meet  and  mingle  in  the  ill-defined  present. 
The  passage  of  nature  which  is  only  another  name  for 
the  creative  force  of  existence  has  no  narrow  ledge  of 
definite  instantaneous  present  within  which  to  operate. 
Its  operative  presence  which  is  now  urging  nature 
forward  must  be  sought  for  throughout  the  whole,  in 
the  remotest  past  as  well  as  in  the  narrowest  breadth  of 
any  present  duration.  Perhaps  also  in  the  unrealised  ' 
future.  Perhaps  also  in  the  future  which  might  be  as  i 
well  as  the  actual  future  which  will  be.  It  is  impossible 
to  meditate  on  time  and  the  mystery  of  the  creative 
passage  of  nature  without  an  overwhelming  emotion 
at  the  limitations  of  human  intelligence. 


CHAPTER  IV 

THE  METHOD  OF  EXTENSIVE 
ABSTRACTION 

To-day's  lecture  must  commence  with  the  consideration 
of  Hmited  events.  We  shall  then  be  in  a  position  to 
enter  upon  an  investigation  of  the  factors  in  nature 
which  are  represented  by  our  conception  of  space. 

The  duration  which  is  the  immediate  disclosure  of 
our  sense-awareness  is  discriminated  into  parts.  There 
is  the  part  which  is  the  life  of  all  nature  within  a  room, 
and  there  is  the  part  which  is  the  life  of  all  nature 
within  a  table  in  the  room.  These  parts  are  limited 
events.  They  have  the  endurance  of  the  present  duration, 
and  they  are  parts  of  it.  But  whereas  a  duration  is  an 
unlimited  whole  and  in  a  certain  limited  sense  is  all 
that  there  is,  a  limited  event  possesses  a  completely 
defined  limitation  of  extent  which  is  expressed  for  us 
in  spatio-temporal  terms. 

We  are  accustomed  to  associate  an  event  with  a  certain 
melodramatic  quality.  If  a  man  is  run  over,  that  is  an 
event  comprised  within  certain  spatio-temporal  limits. 
We  are  not  accustomed  to  consider  the  endurance  of 
the  Great  Pyramid  throughout  any  definite  day  as  an 
event.  But  the  natural  fact  which  is  the  Great  Pyramid 
throughout  a  day,  meaning  thereby  all  nature  within  it, 
is  an  event  of  the  same  character  as  the  man's  accident, 
meaning  thereby  all  nature  with  spatio-temporal  limita- 
tions so  as  to  include  the  man  and  the  motor  during  the 
period  when  they  were  in  contact. 


CH.iv]  METHOD  OF  EXTENSIVE  ABSTRACTION  75 

We  are  accustomed  to  analyse  these  events  into  three 
factors,  time,  space,  and  material.  In  fact,  we  at  once 
apply  to  them  the  concepts  of  the  materialistic  theory 
of  nature.  I  do  not  deny  the  utility  of  this  analysis  for 
the  purpose  of  expressing  important  laws  of  nature. 
What  I  am  denying  is  that  anyone  of  these  factors  is 
posited  for  us  in  sense-awareness  in  concrete  inde- 
pendence. We  perceive  one  unit  factor  in  nature;  and 
this  factor  is  that  something  is  going  on  then — there. 
For  example,  w^  perceive  the  going-on  of  the  Great 
Pyramid  in  its  relations  to  the  goings-on  of  the  sur- 
rounding Egyptian  events.  We  are  so  trained,  both  by 
language  and  by  formal  teaching  and  by  the  resulting 
convenience,  to  express  our  thoughts  in  terms  of  this 
materialistic  analysis  that  intellectually  we  tend  to 
ignore  the  true  unity  of  the  factor  really  exhibited  in 
sense-awareness.  It  is  this  unit  factor,  retaining  in 
itself  the  passage  of  nature,  which  is  the  primary 
concrete  element  discriminated  in  nature.  These 
primary  factors  are  what  I  mean  by  events. 

Events  are  the  field  of  a  two-termed  relation,  namely 
the  relation  of  extension  which  was  considered  in  the 
last  lecture.  Events  are  the  things  related  by  the 
relation  of  extension.  If  an  event  A  extends  over  an 
event  B,  then  B  is  *part  of '  ^,  and  ^  is  a  *  whole  of 
which  5  is  a  part.  Whole  and  part  are  invariably  used 
in  these  lectures  in  this  definite  sense.  It  follows  that 
in  reference  to  this  relation  any  two  events  A  and  B 
may  have  any  one  of  four  relations  to  each  other, 
namely  (i)  A  may  extend  over  J5,  or  (ii)  B  may  extend 
over  A,  or  (iii)  A  and  B  may  both  extend  over  some 
third  event  C,  but  neither  over  the  other,  or  (iv)  A 
and  B  may  be  entirely  separate.  These  alternatives  can 


76  THE  CONCEPT  OF  NATURE  [ch. 

obviously  be  illustrated  by  Euler's  diagrams  as  they 
appear  in  logical  textbooks. 

The  continuity  of  nature  is  the  continuity  of  events. 
This  continuity  is  merely  the  name  for  the  aggregate 
of  a  variety  of  properties  of  events  in  connexion  with 
the  relation  of  extension. 

In  the  first  place,  this  relation  is  transitive;  secondly, 
every  event  contains  other  events  as  parts  of  itself; 
thirdly  every  event  is  a  part  of  other  events;  fourthly 
given  any  two  finite  events  there  are  events  each  of 
which  contains  both  of  them  as  parts ;  and  fifthly  there 
is  a  special  relation  between  events  which  I  term 
*  junction.' 

Two  events  have  junction  when  there  is  a  third  event 
of  which  both  events  are  parts,  and  which  is  such  that 
no  part  of  it  is  separated  from  both  of  the  two  given 
events.  Thus  two  events  with  junction  make  up  exactly 
one  event  which  is  in  a  sense  their  sum. 

Only  certain  pairs  of  events  have  this  property.  In 
general  any  event  containing  two  events  also  contains 
parts  which  are  separated  from  both  events. 

There  is  an  alternative  definition  of  the  junction  of 
two  events  which  I  have  adopted  in  my  recent  book^. 
Two  events  have  junction  when  there  is  a  third  event 
such  that  (i)  it  overlaps  both  events  and  (ii)  it  has  no 
part  which  is  separated  from  both  the  given  events.  If 
either  of  these  alternative  definitions  is  adopted  as  the 
definition  of  junction,  the  other  definition  appears  as 
an  axiom  respecting  the  character  of  junction  as  we 
know  it  in  nature.  But  we  are  not  thinking  of  logical 
definition  so  much  as  the  formulation  of  the  results 
of  direct  observation.    There  is  a  certain  continuity 

^  Cf.  Enquiry. 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    77 

inherent  in  the  observed  unity  of  an  event,  and  these 
tv^o  definitions  of  junction  are  really  axioms  based 
on  observation  respecting  the  character  of  this  con- 
tinuity. 

The  relations  of  vv^hole  and  part  and  of  overlapping 
are  particular  cases  of  the  junction  of  events.  But  it 
is  possible  for  events  to  have  junction  vi^hen  they  are 
separate  from  each  other;  for  example,  the  upper  and 
the  lovvrer  part  of  the  Great  Pyramid  are  divided  by  some 
imaginary  horizontal  plane. 

The  continuity  v^hich  nature  derives  from  events 
has  been  obscured  by  the  illustrations  w^hich  I  have 
been  obliged  to  give.  For  example  I  have  taken  the 
existence  of  the  Great  Pyramid  as  a  fairly  v^ell-knov^n 
fact  to  w^hich  I  could  safely  appeal  as  an  illustration. 
This  is  a  type  of  event  v^hich  exhibits  itself  to  us  as  the 
situation  of  a  recognisable  object ;  and  in  the  example; 
chosen  the  object  is  so  vvridely  recognised  that  it  has 
received  a  name.  An  object  is  an  entity  of  a  different 
type  from  an  event.  For  example,  the  event  w^hich  is 
the  life  of  nature  w^ithin  the  Great  Pyramid  yesterday 
and  to-day  is  divisible  into  two  parts,  namely  the  Great 
Pyramid  yesterday  and  the  Great  Pyramid  to-day.  But 
the  recognisable  object  w^hich  is  also  called  the  Great 
Pyramid  is  the  same  object  to-day  as  it  v^as  yesterday. 
I  shall  have  to  consider  the  theory  of  objects  in  another 
lecture. 

The  w^hole  subject  is  invested  w^ith  an  unmerited  \  ? 
air  of  subtlety  by  the  fact  that  vv^hen  the  event  is  the  f^^  1 
situation  of  a  well-marked  object,  we  have  no  language  j  -^^^ 
to  distinguish  the  event  from  the  object.  In  the  easel '(jJ^*'^ 
of  the  Great  Pyramid,  the  object  is  the  perceived  unit  k  ^^j^ 
entity  which  as  perceived  remains  self-identical  through-  I  .j^j^ 


78  THE  CONCEPT  OF  NATURE  [ch. 

out  the  ages ;  while  the  whole  dance  of  molecules  and 
the  shifting  play  of  the  electromagnetic  field  are 
ingredients  of  the  event.  An  object  is  in  a  sense  out 
''  of  time.  It  is  only  derivatively  in  time  by  reason  of  its 
having  the  relation  to  events  which  I  term  *  situation.' 
This  relation  of  situation  will  require  discussion  in  a 
subsequent  lecture. 

The  point  which  I  want  to  make  now  is  that  being  the 
situation  of  a  well-marked  object  is  not  an  inherent 
necessity  for  an  event.  Wherever  and  whenever  some- 
thing is  going  on,  there  is   an   event.    Furthermore 
*  wherever  and  whenever '  in  themselves  presuppose  an 
event,  for  space  and  time  in  themselves  are  abstractions 
from  events.    It  is  therefore  a  consequence  of  this 
doctrine  that  something  is  always  going  on  everywhere, 
even  in  so-called  empty  space.  This  conclusion  is  in 
accord  with  modern  physical  science  which  presupposes 
the  play  of  an  electromagnetic  field  throughout  space 
and  time.  This  doctrine  of  science  has  been  thrown  into 
the  materialistic  form  of  an  all-pervading  ether.    But 
the  ether  is  evidently  a  mere  idle  concept — inthephraseo- 
f^y^  logy  which   Bacon   applied   to   the   doctrine  of  final 
I  causes,  it  is  a  barren  virgin.   Nothing  is  deduced  from 
it;  and  the  ether  merely  subserves  the  purpose  of 
;  satisfying  the  demands  of  the  materialistic  theory.  The 
I  important  concept  is  that  of  the  shifting  facts  of  the 
j  fields  of  force.  This  is  the  concept  of  an  ether  of  events 
which  should  be  substituted  for  that  of  a  material 
ether. 

It  requires  no  illustration  to  assure  you  that  an  event 
is  a  complex  fact,  and  the  relations  between  two  events 
form  an  almost  impenetrable  maze.  The  clue  discovered 
by  the  common  sense  of  mankind  and  systematically 


IV]     METHOD  OF  EXTENSIVE  ABSTRACTION    79 

utilised  in  science  is  what  I  have  elsewhere  ^  called  the 
law  of  convergence  to  simplicity  by  diminution  of 
extent. 

If  A  and  B  are  two  events,  and  A'  is  part  of  A  and 
B'  is  part  of  By  then  in  many  respects  the  relations 
between  the  parts  A'  and  B'  will  be  simpler  than  the 
relations  between  A  and  B.  This  is  the  principle  which 
presides  over  all  attempts  at  exact  observation. 

The  first  outcome  of  the  systematic  use  of  this  law 
has  been  the  formulation  of  the  abstract  concepts  of 
Time  and  Space.  In  the  previous  lecture  I  sketched 
how  the  principle  was  applied  to  obtain  the  time-series. 
I  now  proceed  to  consider  how  the  spatial  entities  are 
obtained  by  the  same  method.  The  systematic  pro- 
cedure is  identical  in  principle  in  both  cases,  and  I 
have  called  the  general  type  of  procedure  the  *  method 
of  extensive  abstraction.' 

You  will  remember  that  in  my  last  lecture  I  defined 
the  concept  of  an  abstractive  set  of  durations.  This 
definition  can  be  extended  so  as  to  apply  to  any  events, 
limited  events  as  well  as  durations.  The  only  change 
that  is  required  is  the  substitution  of  the  word  *  event ' 
for  the  word  '  duration.'  Accordingly  an  abstractive  set 
of  events  is  any  set  of  events  which  possesses  the  two 
properties,  (i)  of  any  two  members  of  the  set  one  con- 
tains the  other  as  a  part,  and  (ii)  there  is  no  event  which 
is  a  common  part  of  every  member  of  the  set.  Such  a 
set,  as  you  will  remember,  has  the  properties  of  the 
Chinese  toy  which  is  a  nest  of  boxes,  one  within  the 
other,  with  the  difference  that  the  toy  has  a  smallest 
box,  while  the  abstractive  class  has  neither  a  smallest 

^  Cf.  Organisation  of  Thought y  pp.  146  et  seq.  Williams  and 
Norgate,  19 17. 


8o  THE  CONCEPT  OF  NATURE  [ch. 

event  nor  does  it  converge  to  a  limiting  event  which  is 
not  a  member  of  the  set. 

Thus,  so  far  as  the  abstractive  sets  of  events  are  con- 
cerned, an  abstractive  set  converges  to  nothing.  There 
is  the  set  with  its  members  growing  indefinitely  smaller 
and  smaller  as  we  proceed  in  thought  towards  the 
smaller  end  of  the  series;  but  there  is  no  absolute 
minimum  of  any  sort  which  is  finally  reached.  In  fact 
the  set  is  just  itself  and  indicates  nothing  else  in  the 
way  of  events,  except  itself.  But  each  event  hasjan 
intrinsi^^c  characte^^  the  way  of  being  a  situation  of 
objects  and  of  having  parts  which  are  situations  of 
objects  and — to  state  the  matter  more  generally — in  the 
way  of  being  a  field  of  the  life  of  nature.  This  character 
can  be  defined  by  quantitative  expressions  expressing 
relations  between  various  quantities  intrinsic  to  the 
event  or  between  such  quantities  and  other  quantities 
intrinsic  to  other  events.  In  the  case  of  events  of  con- 
siderable spatio-temporal  extension  this  set  of  quanti- 
tative expressions  is  of  bewildering  complexity.  If 
e  be  an  event,  let  us  denote  by  q  (e)  the  set  of  quanti- 
tative expressions  defining  its  character  including  its 
connexions  with  the  rest  of  nature.  Let  ^i,  ^2>  ^3>  ^tc. 
be  an  abstractive  set,  the  members  being  so  arranged 
that  each  member  such  as  e^  extends  over  all  the  suc- 
ceeding members  such  as  ^^+1,  ^n+2>  and  so  on.  Then 
corresponding  to  the  series 

^l>  ^2»  ^3>  •••>  ^w)  ^w+l>   •••> 

there  is  the  series 

(I  (^i)»  ^  (^2)»  9.  (^3)»  •••,  (I  W,  ^  K+i),  .... 
Call  the  series  of  events  s  and  the  series  of  quanti- 
tative expressions  q  {$),  The  series  s  has  no  last  term  and 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    8i 

no  events  which  are  contained  in  every  member  of  the 
series.  Accordingly  the  series  of  events  converges  to 
nothing.  It  is  just  itself.  Also  the  series  q  {s)  has  no 
last  term.  But  the  sets  of  homologous  quantities 
running  through  the  various  terms  of  the  series  do 
converge  to  definite  limits.  For  example  if  Q^  be  a 
quantitative  measurement  found  in  q  (^j),  and  Q^  the 
homologue  to  Q^  to  be  found  in  q  {e^,  and  Q^  the 
homologue  to  Q^  and  ^2  to  be  found  in  q  (^3),  and  so  on, 
then  the  series 

6l>  Q^y  Qz^  •••>  Qny  Qn+l^  •••> 

though  it  has  no  last  term,  does  in  general  converge  to 
a  definite  limit.  Accordingly  there  is  a  class  of  limits 
/  {s)  w^hich  is  the  class  of  the  limits  of  those  members  of 
<Z(^w)  which  have  homologues  throughout  the  series  q{s) 
as  n  indefinitely  increases.  We  can  represent  this  state- 
ment diagrammatically  by  using  an  arrovv^  {■*)  to  mean 
*  converges  to.'   Then 

^1,  ^2,  ^3»  •••>  ^ny  ^n+i,  ...  -^  nothing, 
and 

q  (^i)>  9  (^2)>  q  (^3),  ...,  ^  K),  q  K-m),  ...  -  / (s). 

The  mutual  relations  between  the  limits  in  the  set 
l{s),  and  also  between  these  limits  and  the  limits  in 
other  sets  l{s'),  l{s"),  ...,  which  arise  from  other 
abstractive  sets  s\  s",  etc.,  have  a  peculiar  simplicity. 

Thus  the  set  s  does  indicate  an  ideal  simplicity  of 
natural  relations,  though  this  simplicity  is  not  the 
character  of  any  actual  event  in  s.  We  can  make  an 
approximation  to  such  a  simpHcity  which,  as  estimated 
numerically,  is  as  close  as  we  like  by  considering  an 
event  which  is  far  enough  down  the  series  towards  the 
small  end.  It  will  be  noted  that  it  is  the  infinite  series, 

W.N.  6 


82  THE  CONCEPT  OF  NATURE  [ch. 

as  it  stretches  away  in  unending  succession  towards 
the  small  end,  which  is  of  importance.  The  arbitrarily 
large  event  with  which  the  series  starts  has  no  importance 
at  all.  We  can  arbitrarily  exclude  any  set  of  events  at 
the  big  end  of  an  abstractive  set  without  the  loss  of 
any  important  property  to  the  set  as  thus  modified. 

I  call  the  limiting  character  of  natural  relations  which 
is  indicated  by  an  abstractive  set,  the '  intrinsic  character ' 
of  the  set;  also  the  properties,  connected  with  the 
relation  of  whole  and  part  as  concerning  its  members, 
by  which  an  abstractive  set  is  defined  together  form  what 
I  call  its  *  extrinsic  character.'  The  fact  that  the  ex- 
trinsic character  of  an  abstractive  set  determines  a 
definite  intrinsic  character  is  the  reason  of  the  import- 
ance of  the  precise  concepts  of  space  and  time.  This 
emergence  of  a  definite  intrinsic  character  from  an 
abstractive  set  is  the  precise  meaning  of  the  law  of 
convergence. 

For  example,  we  see  a  train  approaching  during  a 
minute.  The  event  which  is  the  life  of  nature  within 
that  train  during  the  minute  is  of  great  complexity  and 
the  expression  of  its  relations  and  of  the  ingredients 
of  its  character  baffles  us.  If  we  take  one  second  of 
that  minute,  the  more  limited  event  which  is  thus 
obtained  is  simpler  in  respect  to  its  ingredients,  and 
shorter  and  shorter  times  such  as  a  tenth  of  that  second, 
or  a  hundredth,  or  a  thousandth — so  long  as  we  have  a 
definite  rule  giving  a  definite  succession  of  diminishing 
events — give  events  whose  ingredient  characters  con- 
verge to  the  ideal  simplicity  of  the  character  of  the  train 
at  a  definite  instant.  Furthermore  there  are  different 
types  of  such  convergence  to  simplicity.  For  example, 
we  can  converge  as  above  to  the  limiting  character 


IV]     METHOD  OF  EXTENSIVE  ABSTRACTION    83 

expressing  nature  at  an  instant  within  the  whole  volume 
of  the  train  at  that  instant,  or  to  nature  at  an  instant 
within  some  portion  of  that  volume — for  example 
within  the  boiler  of  the  engine — or  to  nature  at  an 
instant  on  some  area  of  surface,  or  to  nature  at  an  instant 
on  some  line  within  the  train,  or  to  nature  at  an  instant 
at  some  point  of  the  train.  In  the  last  case  the  simple 
limiting  characters  arrived  at  will  be  expressed  as 
densities,  specific  gravities,  and  types  of  material. 
Furthermore  we  need  not  necessarily  converge  to  an 
abstraction  which  involves  nature  at  an  instant.  We 
may  converge  to  the  physical  ingredients  of  a  certain 
point  track  throughout  the  whole  minute.  Accordingly 
there  are  different  types  of  extrinsic  character  of  con- 
vergence which  lead  to  the  approximation  to  different 
types  of  intrinsic  characters  as  limits. 

We  now  pass  to  the  investigation  of  possible  con- 
nexions between  abstractive  sets.  One  set  may  *  cover' 
another.  I  define  *  covering'  as  follows:  An  abstractive 
set  p  covers  an  abstractive  set  q  when  every  member  of 
p  contains  as  its  parts  some  members  of  q.  It  is  evident 
that  if  any  event  e  contains  as  a  part  any  member  of 
the  set  q,  then  owing  to  the  transitive  property  of  ex- 
tension every  succeeding  member  of  the  small  end  of  q 
is  part  of  ^.  In  such  a  case  I  will  say  that  the  abstractive 
set  q  *  inheres  in '  the  event  e.  Thus  when  an  abstractive 
set  p  covers  an  abstractive  set  q,  the  abstractive  set  q 
inheres  in  every  member  of/). 

Two  abstractive  sets  may  each  cover  the  other.  When 
this  is  the  case  I  shall  call  the  two  sets  *  equal  in  ab- 
stractive force.'  When  there  is  no  danger  of  misunder- 
standing I  shall  shorten  this  phrase  by  simply  saying 
that  the  two  abstractive  sets  are  *  equal.'  The  possibility 

6—2 


84  THE  CONCEPT  OF  NATURE  [CH. 

of  this  equality  of  abstractive  sets  arises  from  the  fact 
that  both  sets,  p  and  ^,  are  infinite  series  towards  their 
small  ends.  Thus  the  equality  means,  that  given  any 
event  x  belonging  to  p,  we  can  always  by  proceeding 
far  enough  towards  the  small  end  of  q  find  an  event  y 
which  is  part  of  x,  and  that  then  by  proceeding  far 
enough  towards  the  small  end  of  ^  we  can  find  an  event  z 
which  is  part  oiy,  and  so  on  indefinitely. 
*.  /  The  importance  of  the  equality  of  abstractive  sets 
•^"^^  arises  from  the  assumption  that  the  intrinsic  characters 
of  the  two  sets  are  identical.  If  this  were  not  the  case 
exact  observation  would  be  at  an  end. 

It  is  evident  that  any  two  abstractive  sets  which  are 
equal  to  a  third  abstractive  set  are  equal  to  each  other. 
An  *  abstractive  element'  is  the  whole  group  of  ab- 
stractive sets  which  are  equal  to  any  one  of  themselves. 
Thus  all  abstractive  sets  belonging  to  the  same  element 
are  equal  and  converge  to  the  same  intrinsic  character. 
Thus  an  abstractive  element  is  the  group  of  routes  of 
approximation  to  a  definite  intrinsic  character  of  ideal 
simplicity  to  be  found  as  a  limit  among  natural  facts. 

If  an  abstractive  set  p  covers  an  abstractive  set  q,  then 
any  abstractive  set  belonging  to  the  abstractive  element 
of  which  /)  is  a  member  will  cover  any  abstractive  set 
belonging  to  the  element  of  which  ^  is  a  member. 
Accordingly  it  is  useful  to  stretch  the  meaning  of  the 
term  *  covering,'  and  to  speak  of  one  abstractive  element 

*  covering '  another  abstractive  element.  If  we  attempt  in 
like  manner  to  stretch  the  term  *  equal '  in  the  sense  of 

*  equal  in  abstractive  force,'  it  is  obvious  that  an  ab- 
stractive element  can  only  be  equal  to  itself.  Thus  an 
abstractive  element  has  a  unique  abstractive  force  and  is 
the  construct  from  events  which  represents  one  definite 


IV]     METHOD  OF  EXTENSIVE  ABSTRACTION    85 

intrinsic  character  which  is  arrived  at  as  a  Hmit  by  the 
use  of  the  principle  of  convergence  to  simpHcity  by 
diminution  of  extent. 

When  an  abstractive  element  A  covers  an  abstractive 
element  B,  the  intrinsic  character  of  ^  in  a  sense 
includes  the  intrinsic  character  of  B,  It  results  that 
statements  about  the  intrinsic  character  of  B  are  in  a 
sense  statements  about  the  intrinsic  character  of  A; 
but  the  intrinsic  character  of  A  is  more  complex  than 
that  of  B. 

The  abstractive  elements  form  the  fundamental 
elements  of  space  and  time,  and  we  now  turn  to  the 
consideration  of  the  properties  involved  in  the  formation 
of  special  classes  of  such  elements.  In  my  last  lecture 
I  have  already  investigated  one  class  of  abstractive 
elements,  namely  moments.  Each  moment  is  a  group 
of  abstractive  sets,  and  the  events  which  are  members 
of  these  sets  are  all  members  of  one  family  of  durations. 
The  moments  of  one  family  form  a  temporal  series; 
and,  allowing  the  existence  of  different  families  of 
moments,  there  will  be  alternative  temporal  series  in 
nature.  Thus  the  method  of  extensive  abstraction  ex- 
plains the  origin  of  temporal  series  in  terms  of  the 
immediate  facts  of  experience  and  at  the  same  time 
allows  for  the  existence  of  the  alternative  temporal 
series  which  are  demanded  by  the  modern  theory  of 
electromagnetic  relativity. 

We  now  turn  to  space.  The  first  thing  to  do  is  to 
get  hold  of  the  class  of  abstractive  elements  which  are 
in  some  sense  the  points  of  space.  Such  an  abstractive 
element  must  in  some  sense  exhibit  a  convergence  to 
an  absolute  minimum  of  intrinsic  character.  Euclid 
has  expressed  for  all  time  the  general  idea  of  a  point, 


86  THE  CONCEPT  OF  NATURE  [ch. 

as  being  without  parts  and  without  magnitude.  It  is 
this  character  of  being  an  absolute  minimum  which  we 
want  to  get  at  and  to  express  in  terms  of  the  extrinsic 
characters  of  the  abstractive  sets  which  make  up  a  point. 
Furthermore,  points  which  are  thus  arrived  at  repre- 
sent the  ideal  of  events  without  any  extension,  though 
there  are  in  fact  no  such  entities  as  these  ideal  events. 
These  points  will  not  be  the  points  of  an  external  time- 
less space  but  of  instantaneous  spaces.  We  ultimately 
want  to  arrive  at  the  timeless  space  of  physical  science, 
and  also  of  common  thought  which  is  now  tinged  with 
the  concepts  of  science.  It  will  be  convenient  to  reserve 
the  term  *  point'  for  these  spaces  when  we  get  to 
them.  I  will  therefore  use  the  name  *  event-particles ' 
for  the  ideal  minimum  limits  to  events.  Thus  an 
event-particle  is  an  abstractive  element  and  as  such  is 
a  group  of  abstractive  sets ;  and  a  point — namely  a  point 
of  timeless  space — ^will  be  a  class  of  event-particles. 

Furthermore  there  is  a  separate  timeless  space  corre- 
sponding to  each  separate  temporal  series,  that  is  to 
each  separate  family  of  durations.  We  will  come  back 
to  points  in  timeless  spaces  later.  I  merely  mention 
them  now  that  we  may  understand  the  stages  of  our 
investigation.  The  totality  of  event-particles  will  form  a 
four-dimensional  manifold,  the  extra  dimension  arising 
from  time — in  other  words — arising  from  the  points  of 
a  timeless  space  being  each  a  class  of  event-particles. 

The  required  character  of  the  abstractive  sets  which 
form  event-particles  would  be  secured  if  we  could  define 
them  as  having  the  property  of  being  covered  by  any 
abstractive  set  which  they  cover.  For  then  any  other 
abstractive  set  which  an  abstractive  set  of  an  event- 
particle  covered,  would  be   equal  to   it,   and  would 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    87 

therefore  be  a  member  of  the  same  event-particle. 
Accordingly  an  event-particle  could  cover  no  other 
abstractive  element.  This  is  the  definition  which  I 
originally  proposed  at  a  congress  in  Paris  in  1914^. 
There  is  however  a  difficulty  involved  in  this  definition 
if  adopted  without  some  further  addition,  and  I  am  now 
not  satisfied  with  the  way  in  which  I  attempted  to  get 
over  that  difficulty  in  the  paper  referred  to. 

The  difficulty  is  this :  When  event-particles  have  once 
been  defined  it  is  easy  to  define  the  aggregate  of  event- 
particles  forming  the  boundary  of  an  event ;  and  thence 
to  define  the  point-contact  at  their  boundaries  possible 
for  ^  pair  of  events  of  which  one  is  part  of  the  other. 
We  can  then  conceive  all  the  intricacies  of  tangency. 
In  particular  we  can  conceive  an  abstractive  set  of 
which  all  the  members  have  point-contact  at  the  same 
event-particle.  It  is  then  easy  to  prove  that  there  will 
be  no  abstractive  set  with  the  property  of  being 
covered  by  every  abstractive  set  which  it  covers.  I  state 
this  difficulty  at  some  length  because  its  existence  guides 
the  development  of  our  line  of  argument.  We  have  got 
to  annex  some  condition  to  the  root  property  of  being 
covered  by  any  abstractive  set  which  it  covers.  When 
we  look  into  this  question  of  suitable  conditions  we  find 
that  in  addition  to  event-particles  all  the  other  relevant 
spatial  and  spatio-temporal  abstractive  elements  can 
be  defined  in  the  same  way  by  suitably  varying  the 
conditions.  Accordingly  we  proceed  in  a  general  way 
suitable  for  employment  beyond  event-particles. 

Let  (J  be  the  name  of  any  condition  which  some 
abstractive  sets  fulfil.    I  say  that  an  abstractive  set  is 

1  Cf.  •  La  Theorie  Relationniste  de  TEspace,'  Rev.  de  Mita- 
physique  et  de  Morale ^  vol.  xxiii,  191 6. 


88  THE  CONCEPT  OF  NATURE  [ch. 

*  or -prime'  when  it  has  the  two  properties,  (i)  that  it 
satisfies  the  condition  a  and  (ii)  that  it  is  covered  by 
every  abstractive  set  which  both  is  covered  by  it  and 
satisfies  the  condition  a. 

In  other  words  you  cannot  get  any  abstractive  set 
satisfying  the  condition  a  which  exhibits  intrinsic 
character  more  simple  than  that  of  a  o- -prime. 

There  are  also  the  correlative  abstractive  sets  which 
I  call  the  sets  of  a-antiprimes.  An  abstractive  set  is  a 
a-antiprime  when  it  has  the  two  properties,  (i)  that  it 
satisfies  the  condition  a  and  (ii)  that  it  covers  every 
abstractive  set  which  both  covers  it  and  satisfies  the 
condition  a.  In  other  words  you  cannot  get  any  ab- 
stractive set  satisfying  the  condition  o-  which  exhibits 
an  intrinsic  character  more  complex  than  that  of  a 
cr-antiprime. 

The  intrinsic  character  of  a  cr -prime  has  a  certain 
minimum  of  fullness  among  those  abstractive  sets  which 
are  subject  to  the  condition  of  satisfying  a;  whereas 
the  intrinsic  character  of  a  a-antiprime  has  a  corre- 
sponding maximum  of  fullness,  and  includes  all  it  can 
in  the  circumstances. 

Let  us  first  consider  what  help  the  notion  of  anti- 
primes  could  give  us  in  the  definition  of  moments 
which  we  gave  in  the  last  lecture.  Let  the  condition 
or  be  the  property  of  being  a  class  whose  members  are 
all  durations.  An  abstractive  set  which  satisfies  this 
condition  is  thus  an  abstractive  set  composed  wholly 
of  durations.  It  is  convenient  then  to  define  a  moment 
as  the  group  of  abstractive  sets  which  are  equal  to  some 
a-antiprime,  where  the  condition  a  has  this  special 
meaning.  It  will  be  found  on  consideration  (i)  that 
each  abstractive  set  forming  a  moment  is  a  o--antiprime. 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    89 

where  (j  has  this  special  meaning,  and  (ii)  that  we  have 
excluded  from  membership  of  moments  abstractive 
sets  of  durations  which  all  have  one  common  boundary, 
either  the  initial  boundary  or  the  final  boundary.  We 
thus  exclude  special  cases  which  are  apt  to  confuse 
general  reasoning.  The  new  definition  of  a  moment, 
which  supersedes  our  previous  definition,  is  (by  the  aid 
of  the  notion  of  antiprimes)  the  more  precisely  drawn 
of  the  two,  and  the  more  useful. 

The  particular  condition  which  *(j'  stood  for  in  the 
definition  of  moments  included  something  additional 
to  anything  which  can  be  derived  from  the  bare  notion 
of  extension.  A  duration  exhibits  for  thought  a  totality. 
The  notion  of  totality  is  something  beyond  that  of 
extension,  though  the  two  are  interwoven  in  the  notion 
of  a  duration. 

In  the  same  way  the  particular  condition  '  a '  required 
for  the  definition  of  an  event-particle  must  be  looked  for 
beyond  the  mere  notion  of  extension.  The  same  remark 
is  also  true  of  the  particular  conditions  requisite  for  the 
other  spatial  elements.  This  additional  notion  is  ob- 
tained by  distinguishing  between  the  notion  of  *posi-, 
tion '  and  the  notion  of  convergence  to  an  ideal  zero  of 
extension  as  exhibited  by  an  abstractive  set  of  events. 

In  order  to  understand  this  distinction  consider  a 
point  of  the  instantaneous  space  which  we  conceive 
as  apparent  to  us  in  an  almost  instantaneous  glance. 
This  point  is  an  event-particle.  It  has  two  aspects.  In 
one  aspect  it  is  there,  where  it  is.  This  is  its  position  in 
the  space.  In  another  aspect  it  is  got  at  by  ignoring  the 
circumambient  space,  and  by  concentrating  attention  on 
the  smaller  and  smaller  set  of  events  which  approximate 
to  it.  This  is  its  extrinsic  character.  Thus  a  point  has 


90  THE  CONCEPT  OF  NATURE  [ch. 

three  characters,  namely,  its  position  in  the  whole 
instantaneous  space,  its  extrinsic  character,  and  its 
intrinsic  character.  The  same  is  true  of  any  other  spatial 
.element.  For  example  an  instantaneous  volume  in 
instantaneous  space  has  three  characters,  namely,  its 
position,  its  extrinsic  character  as  a  group  of  abstractive 
sets,  and  its  intrinsic  character  which  is  the  limit  of 
natural  properties  which  is  indicated  by  any  one  of 
these  abstractive  sets. 

.  Before  we  can  talk  about  position  in  instantaneous 
space,  we  must  evidently  be  quite  clear  as  to  what  we 
mean  by  instantaneous  space  in  itself.  Instantaneous 
space  must  be  looked  for  as  a  character  of  a  moment. 
For  a  moment  is  all  nature  at  an  instant.  It  cannot  be 
the  intrinsic  character  of  the  moment.  For  the  intrinsic 
character  tells  us  the  limiting  character  of  nature  in 
space  at  that  instant.  Instantaneous  space  must  be 
an  assemblage  of  abstractive  elements  considered  in 
their  mutual  relations.  Thus  an  instantaneous  space  is 
the  assemblage  of  abstractive  elements  covered  by  some 
one  moment,  and  it  is  the  instantaneous  space  of  that 
moment. 

We  have  now  to  ask  what  character  we  have  found  in 
nature  which  is  capable  of  according  to  the  elements  of 
an  instantaneous  space  different  qualities  of  position. 
This  question  at  once  brings  us  to  the  intersection  of 
moments,  which  is  a  topic  not  as  yet  considered  in 
these  lectures. 

The  locus  of  intersection  of  two  moments  is  the 
assemblage  of  abstractive  elements  covered  by  both  of 
them.  Now  two  moments  of  the  same  temporal  series 
cannot  intersect.  Two  moments  respectively  of  different 
families  necessarily  intersect.    Accordingly  in  the  in- 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    91 

stantaneous  space  of  a  moment  we  should  expect  the 
fundamental  properties  to  be  marked  by  the  inter- 
sections with  moments  of  other  families.  If  M  be  a 
given  moment,  the  intersection  of  M  with  another 
moment  A  is  an  instantaneous  plane  in  the  instan- 
taneous space  of  M]  and  if  5  be  a  third  moment 
intersecting  both  M  and  A,  the  intersection  of  M  and  B 
is  another  plane  in  the  space  M.  Also  the  common 
intersection  of  ^,  By  and  M  is  the  intersection  of  the 
two  planes  in  the  space  M,  namely  it  is  a  straight  line 
in  the  space  M.  An  exceptional  case  arises  if  B  and  M 
intersect  in  the  same  plane  as  A  and  M.  Furthermore 
if  C  be  a  fourth  moment,  then  apart  from  special  cases 
which  we  need  not  consider,  it  intersects  M  in  a  plane 
which  the  straight  line  {A,  B,  M)  meets.  Thus  there 
is  in  general  a  common  intersection  of  four  moments 
of  different  families.  This  common  intersection  is  an 
assemblage  of  abstractive  elements  which  are  each 
covered  (or  *lie  in')  all  four  moments.  The  three- 
dimensional  property  of  instantaneous  space  comes  to 
this,  that  (apart  from  special  relations  between  the  four 
moments)  any  fifth  moment  either  contains  the  whole 
of  their  common  intersection  or  none  of  it.  No  further 
subdivision  of  the  common  intersection  is  possible  by 
means  of  moments.  The  'all  or  none'  principle  holds. 
This  is  not  an  a  priori  truth  but  an  empirical  fact  of 
nature. 

It  will  be  convenient  to  reserve  the  ordinary  spatial 
terms  *  plane,'  *  straight  line,'  *  point'  for  the  elements 
of  the  timeless  space  of  a  time-system.  Accordingly  an 
instantaneous  plane  in  the  instantaneous  space  of  a 
moment  will  be  called  a  *  level,'  an  instantaneous  straight 
line  will  be  called  a  *rect,'  and  an  instantaneous  point 


92  THE  CONCEPT  OF  NATURE  [ch. 

will  be  called  a  *  punct/  Thus  a  punct  is  the  assemblage 
of  abstractive  elements  which  lie  in  each  of  four  moments 
whose  families  have  no  special  relations  to  each  other. 
Also  if  P  be  any  moment,  either  every  abstractive 
element  belonging  to  a  given  punct  lies  in  P,  or  no 
abstractive  element  of  that  punct  lies  in  P. 

Position  is  the  quality  which  an  abstractive  element 
possesses  in  virtue  of  the  moments  in  which  it  lies.  The 
abstractive  elements  which  lie  in  the  instantaneous 
space  of  a  given  moment  M  are  differentiated  from  each 
other  by  the  various  other  moments  which  intersect  M 
so  as  to  contain  various  selections  of  these  abstractive 
elements.  It  is  this  differentiation  of  the  elements  which 
constitutes  their  differentiation  of  position.  An  ab- 
stractive element  which  belongs  to  a  punct  has  the 
simplest  type  of  position  in  M,  an  abstractive  element 
which  belongs  to  a  rect  but  not  to  a  punct  has  a  more 
complex  quality  of  position,  an  abstractive  element 
which  belongs  to  a  level  and  not  to  a  rect  has  a  still 
more  complex  quality  of  position,  and  finally  the  most 
complex  quality  of  position  belongs  to  an  abstractive 
element  which  belongs  to  a  volume  and  not  to  a  level. 
A  volume  however  has  not  yet  been  defined.  This 
definition  will  be  given  in  the  next  lecture. 

Evidently  levels,  rects,  and  puncts  in  their  capacity 
as  infinite  aggregates  cannot  be  the  termini  of  sense- 
awareness,  nor  can  they  be  limits  which  are  approxi- 
mated to  in  sense-awareness.  Any  one  member  of  a 
level  has  a  certain  quality  arising  from  its  character  as 
also  belonging  to  a  certain  set  of  moments,  but  the  level 
as  a  whole  is  a  mere  logical  notion  without  any  route  of 
approximation  along  entities  posited  in  sense-awareness. 

On  the  other  hand  an  event-particle  is  defined  so  as 


IV]    METHOD  OF  EXTENSIVE  ABSTRACTION    93 

to  exhibit  this  character  of  being  a  route  of  approxi- 
mation marked  out  by  entities  posited  in  sense-aware- 
ness. A  definite  event-particle  is  defined  in  reference 
to  a  definite  punct  in  the  foUov^ing  manner:  Let  the 
condition  a  mean  the  property  of  covering  all  the 
abstractive  elements  which  are  members  of  that  punct ; 
so  that  an  abstractive  set  which  satisfies  the  condition  a 
is  an  abstractive  set  which  covers  every  abstractive 
element  belonging  to  the  punct.  Then  the  definition 
of  the  event-particle  associated  with  the  punct  is  that 
it  is  the  group  of  all  the  cr-primes,  where  a  has  this 
particular  meaning. 

It  is  evident  that — ^with  this  meaning  of  <j — every 
abstractive  set  equal  to  a  cr -prime  is  itself  a  o- -prime. 
Accordingly  an  event-particle  as  thus  defined  is  an 
abstractive  element,  namely  it  is  the  group  of  those 
abstractive  sets  which  are  each  equal  to  some  given 
abstractive  set.  If  we  write  out  the  definition  of  the 
event-particle  associated  with  some  given  punct,  which 
we  will  call  tt,  it  is  as  follows:  The  event-particle  as- 
sociated with  77  is  the  group  of  abstractive  classes  each 
of  which  has  the  two  properties  (i)  that  it  covers  every 
abstractive  set  in  tt  and  (ii)  that  all  the  abstractive  sets 
which  also  satisfy  the  former  condition  as  to  77  and  which 
it  covers,  also  cover  it. 

An  event-particle  has  position  by  reason  of  its 
association  with  a  punct,  and  conversely  the  punct 
gains  its  derived  character  as  a  route  of  approximation 
from  its  association  with  the  event-particle.  These  two 
characters  of  a  point  are  always  recurring  in  any  treat- 
ment of  the  derivation  of  a  point  from  the  observed 
facts  of  nature,  but  in  general  there  is  no  clear  recogni- 
tion of  their  distinction. 


94  THE  CONCEPT  OF  NATURE  [cH. 

The  peculiar  simplicity  of  an  instantaneous  point  has 
a  twofold  origin,  one  connected  with  position,  that  is 
to  say  with  its  character  as  a  punct,  and  the  other  con- 
nected with  its  character  as  an  event-particle.  The 
simplicity  of  the  punct  arises  from  its  indivisibility  by 
a  moment. 

The  simplicity  of  an  event-particle  arises  from  the 
indivisibility  of  its  intrinsic  character.  The  intrinsic 
character  of  an  event-particle  is  indivisible  in  the  sense 
that  every  abstractive  set  covered  by  it  exhibits  the 
same  intrinsic  character.  It  follows  that,  though  there 
are  diverse  abstractive  elements  covered  by  event- 
particles,  there  is  no  advantage  to  be  gained  by  con- 
sidering them  since  we  gain  no  additional  simplicity 
in  the  expression  of  natural  properties. 

These  two  characters  of  simplicity  enjoyed  respec- 
tively by  event-particles  and  puncts  define  a  meaning  for 
Euclid's  phrase,  *  without  parts  and  without  magnitude.' 

It  is  obviously  convenient  to  sweep  away  out  of  our 
thoughts  all  these  stray  abstractive  sets  which  are 
covered  by  event-particles  without  themselves  being 
members  of  them.  They  give  us  nothing  new  in  the 
way  of  intrinsic  character.  Accordingly  we  can  think 
of  rects  and  levels  as  merely  loci  of  event-particles. 
In  so  doing  we  are  also  cutting  out  those  abstractive 
elements  which  cover  sets  of  event-particles,  without 
these  elements  being  event-particles  themselves.  There 
are  classes  of  these  abstractive  elements  which  are  of 
great  importance.  I  will  consider  them  later  on  in  this 
and  in  other  lectures.  Meanwhile  we  will  ignore  them. 
Also  I  will  always  speak  of  *  event-particles '  in  pre- 
ference to  *  puncts,'  the  latter  being  an  artificial  word 
for  which  I  have  no  great  affection. 


IV]     METHOD  OF  EXTENSIVE  ABSTRACTION    95 

Parallelism  among  rects  and  levels  is  now^  explicable. 

Consider  the  instantaneous  space  belonging  to  a 
moment  Ay  and  let  A  belong  to  the  temporal  series  of 
moments  v^hich  I  v^ill  call  a.  Consider  any  other 
temporal  series  of  moments  w^hich  I  v^ill  call  j8.  The 
moments  of  j8  do  not  intersect  each  other  and  they 
intersect  the  moment  ^  in  a  family  of  levels.  None  of 
these  levels  can  intersect,  and  they  form  a  family  of 
parallel  instantaneous  planes  in  the  instantaneous  space 
of  moment  A.  Thus  the  parallelism  of  moments  in  a 
temporal  series  begets  the  parallelism  of  levels  in  an 
instantaneous  space,  and  thence — as  it  is  easy  to  see — 
the  parallelism  of  rects.  Accordingly  the  Euclidean 
property  of  space  arises  from  the  parabolic  property  of 
time.  It  may  be  that  there  is  reason  to  adopt  a  hyper- 
bolic theory  of  time  and  a  corresponding  hyperbolic 
theory  of  space.  Such  a  theory  has  not  been  vi^orked  out, 
so  it  is  not  possible  to  judge  as  to  the  character  of  the 
evidence  v^hich  could  be  brought  forw^ard  in  its  favour. 

The  theory  of  order  in  an  instantaneous  space  is 
immediately  derived  from  time-order.  For  consider  the 
space  of  a  moment  M.  Let  a  be  the  name  of  a  time- 
system  to  w^hich  M  does  not  belong.  Let  A^,  A2,  A^y  etc. 
be  moments  of  a  in  the  order  of  their  occurrences.  Then 
Ai,  A^y  A^y  etc.  intersect  M  in  parallel  levels  Z^,  4,  4,  etc. 
Then  the  relative  order  of  the  parallel  levels  in  the 
space  of  M  is  the  same  as  the  relative  order  of  the  corre- 
sponding moments  in  the  time-system  «.  Any  rect  in 
M  which  intersects  all  these  levels  in  its  set  of  puncts, 
thereby  receives  for  its  puncts  an  order  of  position  on  it. 
So  spatial  order  is  derivative  from  temporal  order. 
Furthermore  there  are  alternative  time-systems,  but 
there  is  only  one  definite  spatial  order  in  each  instan- 


96  THE  CONCEPT  OF  NATURE  [ch. 

taneous  space.  Accordingly  the  various  modes  of 
deriving  spatial  order  from  diverse  time-systems  must 
harmonise  with  one  spatial  order  in  each  instantaneous 
space.  In  this  way  also  diverse  time-orders  are  com- 
parable. 

We  have  two  great  questions  still  on  hand  to  be 
settled  before  our  theory  of  space  is  fully  adjusted. 
One  of  these  is  the  question  of  the  determination  of  the 
methods  of  measurement  within  the  space,  in  other 
words,  the  congruence-theory  of  the  space.  The 
measurement  of  space  will  be  found  to  be  closely 
connected  with  the  measurement  of  time,  with  respect 
to  which  no  principles  have  as  yet  been  determined. 
Thus  our  congruence-theory  will  be  a  theory  both  for 
space  and  for  time.  Secondly  there  is  the  determination 
of  the  timeless  space  which  corresponds  to  any  particular 
time-system  with  its  infinite  set  of  instantaneous  spaces 
in  its  successive  moments.  This  is  the  space — or  rather, 
these  are  the  spaces — of  physical  science.  It  is  very 
usual  to  dismiss  this  space  by  saying  that  this  is  con- 
ceptual. I  do  not  understand  the  virtue  of  these  phrases. 
I  suppose  that  it  is  meant  that  the  space  is  the  concep- 
tion of  something  in  nature.  Accordingly  if  the  space 
of  physical  science  is  to  be  called  conceptual,  I  ask, 
What  in  nature  is  it  the  conception  of?  For  example, 
when  we  speak  of  a  point  in  the  timeless  space  of 
physical  science,  I  suppose  that  we  are  speaking  of 
something  in  nature.  If  we  are  not  so  speaking,  our 
scientists  are  exercising  their  w4ts  in  the  realms  of 
pure  fantasy,  and  this  is  palpably  not  the  case.  This 
demand  for  a  definite  Habeas  Corpus  Act  for  the  pro- 
duction of  the  relevant  entities  in  nature  applies  whether 
space  be  relative  or  absolute.  On  the  theory  of  relative 


IV]     METHOD  OF  EXTENSIVE  ABSTRACTION    97 

space,  it  may  perhaps  be  argued  that  there  is  no  timeless 
space  for  physical  science,  and  that  there  is  only  the 
momentary  series  of  instantaneous  spaces. 

An  explanation  must  then  be  asked  for  the  meaning 
of  the  very  common  statement  that  such  and  such  a 
man  walked  four  miles  in  some  definite  hour.  How  can 
you  measure  distance  from  one  space  into  another 
space?  I  understand  walking  out  of  the  sheet  of  an 
ordnance  map.  But  the  meaning  of  saying  that  Cam- 
bridge at  10  o'clock  this  morning  in  the  appropriate 
instantaneous  space  for  that  instant  is  52  miles  from 
London  at  11  o'clock  this  morning  in  the  appropriate 
instantaneous  space  for  that  instant  beats  me  entirely. 
I  think  that,  by  the  time  a  meaning  has  been  produced 
for  this  statement,  you  will  find  that  you  have  constructed 
what  is  in  fact  a  timeless  space.  What  I  cannot  under- 
stand is  how  to  produce  an  explanation  of  meaning 
without  in  effect  making  some  such  construction.  Also 
I  may  add  that  I  do  not  know  how  the  instantaneous 
spaces  are  thus  correlated  into  one  space  by  any  method 
which  is  available  on  the  current  theories  of  space. 

You  will  have  noticed  that  by  the  aid  of  the  assump- 
tion of  alternative  time-systems,  we  are  arriving  at  an 
explanation  of  the  character  of  space.  In  natural  science 
*  to  explain '  means  merely  to  discover  *  interconnexions.' 
For  example,  in  one  sense  there  is  no  explanation  of  the 
red  which  you  see.  It  is  red,  and  there  is  nothing  else 
to  be  said  about  it.  Either  it  is  posited  before  you  in 
sense-awareness  or  you  are  ignorant  of  the  entity  red. 
But  science  has  explained  red.  Namely  it  has  dis- 
covered interconnexions  between  red  as  a  factor  in 
nature  and  other  factors  in  nature,  for  example  waves  of 
light  which  are  waves  of  electromagnetic  disturbances. 

W.N.  7 


98  THE  CONCEPT  OF  NATURE  [ch.  iv 

There  are  also  various  pathological  states  of  the  body 
which  lead  to  the  seeing  of  red  without  the  occurrence 
of  light  waves.  Thus  connexions  have  been  discovered 
between  red  as  posited  in  sense-awareness  and  various 
other  factors  in  nature.  The  discovery  of  these  con- 
nexions constitutes  the  scientific  explanation  of  our 
vision  of  colour.  In  like  manner  the  dependence  of 
the  character  of  space  on  the  character  of  time  con- 
stitutes an  explanation  in  the  sense  in  which  science 
seeks  to  explain.  The  systematising  intellect  abhors 
bare  facts.  The  character  of  space  has  hitherto  been 
presented  as  a  collection  of  bare  facts,  ultimate  and 
disconnected.  The  theory  which  I  am  expounding 
sweeps  away  this  disconnexion  of  the  facts  of  space. 


CHAPTER  V 

SPACE  AND   MOTION 

The  topic  for  this  lecture  is  the  continuation  of  the 
task  of  explaining  the  construction  of  spaces  as  ab- 
stracts from  the  facts  of  nature.  It  was  noted  at  the 
close  of  the  previous  lecture  that  the  question  of 
congruence  had  not  been  considered,  nor  had  the  con- 
struction of  a  timeless  space  which  should  correlate 
the  successive  momentary  spaces  of  a  given  time-system. 
Furthermore  it  was  also  noted  that  there  were  many 
spatial  abstractive  elements  which  we  had  not  yet 
defined.  We  will  first  consider  the  definition  of  some 
of  these  abstractive  elements,  namely  the  definitions 
of  soHds,  of  areas,  and  of  routes.  By  a  *  route'  I  mean 
a  linear  segment,  whether  straight  or  curved.  The  ex- 
position of  these  definitions  and  the  preliminary  ex- 
planations necessary  will,  I  hope,  serve  as  a  general 
explanation  of  the  function  of  event-particles  in  the 
analysis  of  nature. 

We  note  that  event-particles  have  *  position '  in  respect 
to  each  other.  In  the  last  lecture  I  explained  that 
*  position'  was  quality  gained  by  a  spatial  element  in 
virtue  of  the  intersecting  moments  which  covered  it. 
Thus  each  event-particle  has  position  in  this  sense. 
The  simplest  mode  of  expressing  the  position  in  nature 
of  an  event-particle  is  by  first  fixing  on  any  definite 
time-system.  Call  it  a.  There  will  be  one  moment  of 
the  temporal  series  of  a  which  covers  the  given  event- 
particle.  Thus  the  position  of  the  event-particle  in  the 
temporal  series  a  is  defined  by  this  moment,  which  we 

7—2 


100  THE  CONCEPT  OF  NATURE  [ch. 

will  call  M,  The  position  of  the  particle  in  the  space 
of  M  is  then  fixed  in  the  ordinary  way  by  three  levels 
which  intersect  in  it  and  in  it  only.  This  procedure  of 
fixing  the  position  of  an  event-particle  shows  that  the 
aggregate  of  event-particles  forms  a  four-dimensional 
manifold.    A  finite  event  occupies  a  limited  chunk  of 
this  manifold  in  a  sense  which  I  now  proceed  to  explain. 
Let  e  be  any  given  event.  The  manifold  of  event- 
particles  falls  into  three  sets  in  reference  to  e.    Each 
event-particle  is  a  group  of  equal  abstractive  sets  and 
each  abstractive  set  towards  its  small-end  is  composed 
of  smaller  and  smaller  finite  events.   When  we  select 
from  these  finite  events  which  enter  into  the  make-up 
of  a  given  event-particle  those  which  are  small  enough, 
one  of  three  cases  must  occur.    Either  (i)  all  of  these 
small  events  are  entirely  separate  from  the  given  event  e, 
or  (ii)  all  of  these  small  events  are  parts  of  the  event  e^ 
or  (iii)  all  of  these  small  events  overlap  the  event  e  but 
are  not  parts  of  it.    In  the  first  case  the  event-particle 
will  be  said  to  *lie  outside'  the  event  e,  in  the  second 
case  the  event-particle  will  be  said  to  *lie  inside'  the 
event  e,  and  in  the  third  case  the  event-particle  will  be 
said  to  be  a  *boundary-particle'  of  the  event  e.  Thus  there 
are  three  sets  of  particles,  namely  the  set  of  those  which 
lie  outside  the  event  e,  the  set  of  those  which  lie  inside 
the  event  e,  and  the  boundary  of  the  event  e  which  is 
the  set  of  boundary-particles  of  e.   Since  an  event  is 
four-dimensional,  the  boundary  of  an  event  is  a  three- 
dimensional  manifold.    For  a  finite  event  there  is  a 
continuity  of  boundary;  for  a  duration  the  boundary 
consists  of  those  event-particles  which  are  covered  by 
either  of  the  two  bounding  moments.  Thus  the  boundary 
of  a  duration  consists  of  two  momentary  three-dimen-^ 


V]  SPACE  AND  MOTION  loi 

sional  spaces.  An  event  will  be  said  to  *  occupy'  the 
aggregate  of  event-particles  which  lie  within  it. 

Two  events  which  have  *  junction'  in  the  sense  in 
which  junction  was  described  in  my  last  lecture,  and 
yet  are  separated  so  that  neither  event  either  overlaps 
or  is  part  of  the  other  event,  are  said  to  be  *  adjoined.' 

This  relation  of  adjunction  issues  in  a  peculiar  relation 
between  the  boundaries  of  the  two  events.  The  two 
boundaries  must  have  a  common  portion  which  is  in 
fact  a  continuous  three-dimensional  locus  of  event- 
particles  in  the  four-dimensional  manifold. 

A  three-dimensional  locus  of  event-particles  which 
is  the  common  portion  of  the  boundary  of  two  adjoined 
events  will  be  called  a  *  solid.'  A  solid  may  or  may  not 
lie  completely  in  one  moment.  A  solid  which  does  not 
lie  in  one  moment  will  be  called  *  vagrant.'  A  solid 
which  does  lie  in  one  moment  will  be  called  a  volume. 
A  volume  may  be  defined  as  the  locus  of  the  event- 
particles  in  which  a  moment  intersects  an  event,  pro- 
vided that  the  two  do  intersect.  The  intersection  of  a 
moment  and  an  event  will  evidently  consist  of  those 
event-particles  which  are  covered  by  the  moment  and 
lie  in  the  event.  The  identity  of  the  two  definitions  of  a 
volume  is  evident  when  we  remember  that  an  intersect- 
ing moment  divides  the  event  into  two  adjoined  events. 

A  solid  as  thus  defined,  whether  it  be  vagrant  or  be 
a  volume,  is  a  mere  aggregate  of  event-particles  illus- 
trating a  certain  quality  of  position.  We  can  also  define 
a  solid  as  an  abstractive  element.  In  order  to  do  so  we 
recur  to  the  theory  of  primes  explained  in  the  preceding 
lecture.  Let  the  condition  named  a  stand  for  the  fact 
that  each  of  the  events  of  any  abstractive  set  satisfying  it 
has  all  the  event-particles  of  some  particular  solid  lying 


102  THE  CONCEPT  OF  NATURE  [ch. 

in  it.  Then  the  group  of  all  the  or -primes  is  the  abstractive 
element  which  is  associated  with  the  given  solid.  I  will 
call  this  abstractive  element  the  solid  as  an  abstractive 
element,  and  I  will  call  the  aggregate  of  event-particles 
the  solid  as  a  locus.  The  instantaneous  volumes  in 
instantaneous  space  which  are  the  ideals  of  our  sense- 
perception  are  volumes  as  abstractive  elements.  What 
we  really  perceive  with  all  our  efforts  after  exactness 
are  small  events  far  enough  down  some  abstractive 
set  belonging  to  the  volume  as  an  abstractive  element. 

It  is  difficult  to  know  how  far  we  approximate  to  any 
perception  of  vagrant  solids.  We  certainly  do  not  think 
that  we  make  any  such  approximation.  But  then  our 
thoughts — in  the  case  of  people  who  do  think  about 
such  topics — are  so  much  under  the  control  of  the 
materialistic  theory  of  nature  that  they  hardly  count 
for  evidence.  If  Einstein's  theory  of  gravitation  has  any 
truth  in  it,  vagrant  solids  are  of  great  importance  in 
science.  The  whole  boundary  of  a  finite  event  may  be 
looked  on  as  a  particular  example  of  a  vagrant  solid 
as  a  locus.  Its  particular  property  of  being  closed  pre- 
vents it  from  being  definable  as  an  abstractive  element. 

When  a  moment  intersects  an  event,  it  also  intersects 
the  boundary  of  that  event.  This  locus,  which  is  the 
portion  of  the  boundary  contained  in  the  moment,  is 
the  bounding  surface  of  the  corresponding  volume  of 
that  event  contained  in  the  moment.  It  is  a  two- 
dimensional  locus. 

The  fact  that  every  volume  has  a  bounding  surface  is 
the  origin  of  the  Dedekindian  continuity  of  space. 

Another  event  may  be  cut  by  the  same  moment  in 
another  volume  and  this  volume  will  also  have  its 
boundary.  These  two  volumes  in  the  instantaneous 


V]  SPACE  AND  MOTION  103 

space  of  one  moment  may  mutually  overlap  in  the 
familiar  way  which  I  need  not  describe  in  detail  and  thus 
cut  off  portions  from  each  other's  surfaces.  These  por- 
tions of  surfaces  are  *momental  areas/ 

It  is  unnecessary  at  this  stage  to  enter  into  the  com- 
plexity of  a  definition  of  vagrant  areas.  Their  definition 
is  simple  enough  when  the  four-dimensional  manifold 
of  event-particles  has  been  more  fully  explored  as  to 
its  properties. 

Momental  areas  can  evidently  be  defined  as  abstrac- 
tive elements  by  exactly  the  same  method  as  applied 
to  solids.    We  have  merely  to  substitute  *area*  for  a 

*  solid'  in  the  words  of  the  definition  already  given. 
Also,  exactly  as  in  the  analogous  case  of  a  solid,  what 
we  perceive  as  an  approximation  to  our  ideal  of  an  area 
is  a  small  event  far  enough  down  towards  the  small  end 
of  one  of  the  equal  abstractive  sets  which  belongs  to 
the  area  as  an  abstractive  element. 

Two  momental  areas  lying  in  the  same  moment  can 
cut  each  other  in  a  momental  segment  which  is  not 
necessarily  rectilinear.  Such  a  segment  can  also  be 
defined  as  an  abstractive  element.    It  is  then  called  a 

*  momental  route.'  We  will  not  delay  over  any  general 
consideration  of  these  momental  routes,  nor  is  it 
important  for  us  to  proceed  to  the  still  wider  investiga- 
tion of  vagrant  routes  in  general.  There  are  however  two 
simple  sets  of  routes  which  are  of  vital  importance.  One 
is  a  set  of  momental  routes  and  the  other  of  vagrant 
routes.  Both  sets  can  be  classed  together  as  straight 
routes.  We  proceed  to  define  them  without  any  re- 
ference to  the  definitions  of  volumes  and  surfaces. 

The  two  types  of  straight  routes  will  be  called 
rectilinear  routes  and  stations.    Rectilinear  routes  are 


104  THE  CONCEPT  OF  NATURE  [ch. 

momental  routes  and  stations  are  vagrant  routes. 
Rectilinear  routes  are  routes  which  in  a  sense  He  in 
rects.  Any  two  event-particles  on  a  rect  define  the  set 
of  event-particles  which  lie  between  them  on  that  rect. 
Let  the  satisfaction  of  the  condition  a  by  an  abstractive 
set  mean  that  the  two  given  event-particles  and  the 
event-particles  lying  between  them  on  the  rect  all  lie 
in  every  event  belonging  to  the  abstractive  set.  The 
group  of  or -primes,  where  g  has  this  meaning,  form  an 
abstractive  element.  Such  abstractive  elements  are  recti- 
linear routes.  They  are  the  segments  of  instantaneous 
straight  lines  which  are  the  ideals  of  exact  perception. 
Our  actual  perception,  however  exact,  will  be  the  per- 
ception of  a  small  event  sufficiently  far  down  one  of 
the  abstractive  sets  of  the  abstractive  element. 

A  station  is  a  vagrant  route  and  no  moment  can  inter- 
sect any  station  in  more  than  one  event-particle.  Thus 
a  station  carries  with  it  a  comparison  of  the  positions 
in  their  respective  moments  of  the  event-particles 
covered  by  it.  Rects  arise  from  the  intersection  of 
moments.  But  as  yet  no  properties  of  events  have  been 
mentioned  by  which  any  analogous  vagrant  loci  can 
be  found  out. 

The  general  problem  for  our  investigation  is  to 
determine  a  method  of  comparison  of  position  in  one 
instantaneous  space  with  positions  in  other  instantaneous 
spaces.  We  may  limit  ourselves  to  the  spaces  of  the 
parallel  moments  of  one  time-system.  How  are  positions 
in  these  various  spaces  to  be  compared  ?  In  other  words. 
What  do  we  mean  by  motion.^  It  is  the  fundamental 
question  to  be  asked  of  any  theory  of  relative  space, 
and  like  many  other  fundamental  questions  it  is  apt  to 
be  left  unanswered.   It  is  not  an  answer  to  reply,  that 


V]  SPACE  AND  MOTION  105 

we  all  know  what  we  mean  by  motion.  Of  course  we  V 
do,  so  far  as  sense-awareness  is  concerned.  I  am  asking 
that  your  theory  of  space  should  provide  nature  with 
something  to  be  observed.  You  have  not  settled  the 
question  by  bringing  forward  a  theory  according  to 
which  there  is  nothing  to  be  observed,  and  by  then 
reiterating  that  nevertheless  we  do  observe  this  non- 
existent fact.  Unless  motion  is  something  as  a  fact  in 
nature,  kinetic  energy  and  momentum  and  all  that 
depends  on  these  physical  concepts  evaporate  from  our 
list  of  physical  realities.  Even  in  this  revolutionary  age 
my  conservatism  resolutely  opposes  the  identification 
of  momentum  and  moonshine. 

Accordingly  I  assume  it  as  an  axiom,  that  motion 
is  a  physical  fact.  It  is  something  that  we  perceive  as 
in  nature.  Motion  presupposes  rest.  Until  theory  arose 
to  vitiate  immediate  intuition,  that  is  to  say  to  vitiate 
the  uncriticised  judgments  which  immediately  arise 
from  sense-awareness,  no  one  doubted  that  in  motion 
you  leave  behind  that  which  is  at  rest.  Abraham  in  his 
wanderings  left  his  birthplace  where  it  had  ever  been. 
A  theory  of  motion  and  a  theory  of  rest  are  the  same 
thing  viewed  from  different  aspects  with  altered  em- 
phasis. 

Now  you  cannot  have  a  theory  of  rest  without  in  some 
sense  admitting  a  theory  of  absolute  position.  It  is 
usually  assumed  that  relative  space  implies  that  there  is 
no  absolute  position.  This  is,  according  to  my  creed,  a 
mistake.  The  assumption  arises  from  the  failure  to 
make  another  distinction;  namely,  that  there  may  be 
alternative  definitions  of  absolute  position.  This  possi- 
bility enters  with  the  admission  of  alternative  time- 
systems.   Thus   the   series   of  spaces   in   the   parallel 


io6  THE  CONCEPT  OF  NATURE  [ch. 

moments  of  one  temporal  series  may  have  their  own 
definition  of  absolute  position  correlating  sets  of  event- 
particles  in  these  successive  spaces,  so  that  each  set 
consists  of  event-particles,  one  from  each  space,  all 
with  the  property  of  possessing  the  same  absolute 
position  in  that  series  of  spaces.  Such  a  set  of  event- 
particles  will  form  a  point  in  the  timeless  space  of  that 
time-system.  Thus  a  point  is  really  an  absolute  position 
in  the  timeless  space  of  a  given  time-system. 

But  there  are  alternative  time-systems,  and  each 
time-system  has  its  own  peculiar  group  of  points — that 
is  to  say,  its  own  peculiar  definition  of  absolute  position. 
This  is  exactly  the  theory  which  I  will  elaborate. 

In  looking  to  nature  for  evidence  of  absolute  position 
it  is  of  no  use  to  recur  to  the  four-dimensional  manifold 
of  event-particles.  •  This  manifold  has  been  obtained  by 
the  extension  of  thought  beyond  the  immediacy  of 
observation.  We  shall  find  nothing  in  it  except  what  we 
have  put  there  to  represent  the  ideas  in  thought  which 
i  arise  from  our  direct  sense-awareness  of  nature.  To 
'  find  evidence  of  the  properties  which  are  to  be  found 
in  the  manifold  of  event-particles  we  must  always 
recur  to  the  observation  of  relations  between  events. 
Our  problem  is  to  determine  those  relations  between 
events  which  issue  in  the  property  of  absolute  position 
in  a  timeless  space.  This  is  in  fact  the  problem  of  the 
determination  of  the  very  meaning  of  the  timeless 
spaces  of  physical  science. 

In  reviewing  the  factors  of  nature  as  immediately 
disclosed  in  sense-awareness,  we  should  note  the 
fundamental  character  of  the  percept  of  'being  here.' 
We  discern  an  event  merely  as  a  factor  in  a  determinate 
complex  in  which  each  factor  has  its  own  peculiar  share. 


V]  SPACE  AND  MOTION  107 

There  are  two  factors  which  are  always  ingredient  in 
this  complex,  one  is  the  duration  which  is  represented 
in  thought  by  the  concept  of  all  nature  that  is  present 
now,  and  the  other  is  the  peculiar  locus  standi  for  mind 
involved  in  the  sense-awareness.  This  locus  standi  in 
nature  is  what  is  represented  in  thought  by  the  concept 
of '  here,'  namely  of  an  *  event  here/ 

This  is  the  concept  of  a  definite  factor  in  nature.  This 
factor  is  an  event  in  nature  which  is  the  focus  in  nature 
for  that  act  of  awareness,  and  the  other  events  are 
perceived  as  referred  to  it.  This  event  is  part  of  the 
associated  duration.  I  call  it  the  *  percipient  event.' 
This  event  is  not  the  mind,  that  is  to  say,  not  the  per- 
cipient. It  is  that  in  nature  from  which  the  mind 
perceives.  The  complete  foothold  of  the  mind  in  nature 
is  represented  by  the  pair  of  events,  namely,  the  present 
duration  which  marks  the  *  when '  of  awareness  and  the 
percipient  event  which  marks  the  *  where '  of  awareness 
and  the  *how'  of  awareness.  This  percipient  event  is 
roughly  speaking  the  bodily  life  of  the  incarnate  mind. 
But  this  identification  is  only  a  rough  one.  For  the 
functions  of  the  body  shade  off  into  those  of  other  events 
in  nature ;  so  that  for  some  purposes  the  percipient  event 
is  to  be  reckoned  as  merely  part  of  the  bodily  life  and 
for  other  purposes  it  may  even  be  reckoned  as  more  than 
the  bodily  life.  In  many  respects  the  demarcation  is 
purely  arbitrary,  depending  upon  where  in  a  sliding 
scale  you  choose  to  draw  the  line. 

I  have  already  in  my  previous  lecture  on  Time  dis- 
cussed the  association  of  mind  with  nature.  The  difficulty 
of  the  discussion  lies  in  the  liability  of  constant  factors 
to  be  overlooked.  We  never  note  them  by  contrast 
with  their  absences.  The  purpose  of  a  discussion  of  such 


io8  THE  CONCEPT  OF  NATURE  [ch. 

factors  may  be  described  as  being  to  make  obvious 
things  look  odd.  We  cannot  envisage  them  unless  we 
manage  to  invest  them  with  some  of  the  freshness  which 
is  due  to  strangeness. 

It  is  because  of  this  habit  of  letting  constant  factors 
slip  from  consciousness  that  we  constantly  fall  into  the 
error  of  thinking  of  the  sense-awareness  of  a  particular 
factor  in  nature  as  being  a  two-termed  relation  between 
the  mind  and  the  factor.  For  example,  I  perceive  a 
green  leaf.  Language  in  this  statement  suppresses  all 
reference  to  any  factors  other  than  the  percipient  mind 
and  the  green  leaf  and  the  relation  of  sense-awareness. 
It  discards  the  obvious  inevitable  factors  which  are 
essential  elements  in  the  perception.  I  am  here,  the 
leaf  is  there ;  and  the  event  here  and  the  event  which  is 
the  life  of  the  leaf  there  are  both  embedded  in  a  totality 
of  nature  which  is  now,  and  within  this  totality  there 
are  other  discriminated  factors  which  it  is  irrelevant  to 
mention.  Thus  language  habitually  sets  before  the  mind 
a  misleading  abstract  of  the  indefinite  complexity  of 
the  fact  of  sense-awareness. 

What  I  now  want  to  discuss  is  the  special  relation  of 
the  percipient  event  which  is  ^here'  to  the  duration 
which  is  '  now.'  This  relation  is  a  fact  in  nature,  namely 
the  mind  is  aware  of  nature  as  being  with  these  two 
factors  in  this  relation. 

Within  the  short  present  duration  the  '  here '  of  the 
percipient  event  has  a  definite  meaning  of  some  sort. 
This  meaning  of  'here'  is  the  content  of  the  special 
relation  of  the  percipient  event  to  its  associated  duration. 
I  will  call  this  relation  *  cogredience.'  Accordingly  I  ask 
for  a  description  of  the  character  of  the  relation  of 
cogredience.  The  present  snaps  into  a  past  and  a  present 


v]  SPACE  AND  MOTION  109 

when  the  *  here '  of  cogredience  loses  its  single  deter- 
minate meaning.  There  has  been  a  passage  of  nature 
from  the  *  here '  of  perception  within  the  past  duration 
to  the  different '  here '  of  perception  within  the  present 
duration.     But    the   two    *heres'    of   sense-awareness 
within  neighbouring  durations  may  be  indistinguishable. 
In  this  case  there  has  been  a  passage  from  the  past  to 
the  present,  but  a  more  retentive  perceptive  force  might 
have  retained  the  passing  nature  as  one  complete  present 
instead  of  letting  the  earlier  duration  slip  into  the  past. 
Namely,  the  sense  of  rest  helps  the  integration  of  dura- 
tions into  a  prolonged  present,  and  the  sense  of  motion 
differentiates   nature   into   a   succession   of  shortened 
durations.   As  we  look  out  of  a  railway  carriage  in  an 
express  train,  the  present  is  past  before  reflexion  can 
seize  it.  We  live  in  snippits  too  quick  for  thought.  On 
the  other  hand  the  immediate  present  is  prolonged 
according  as  nature  presents  itself  to  us  in  an  aspect  of 
unbroken  rest.  Any  change  in  nature  provides  ground 
for  a  differentiation  among  durations  so  as  to  shorten 
the  present.    But  there  is  a  great  distinction  between 
self -change  in  nature  and  change  in  external  nature. 
Self-change  in  nature  is  change  in  the  quality  of  the 
standpoint  of  the  percipient  event.    It  is  the  break  up 
of  the  *here'  which  necessitates  the  break  up  of  the 
present  duration.    Change  in  external  nature  is  com- 
patible with  a  prolongation  of  the  present  of  contem- 
plation rooted  in  a  given  standpoint.   What  I  want  to 
bring  out  is  that  the  preservation  of  a  peculiar  relation 
to  a  duration  is  a  necessary  condition  for  the  function 
of  that  duration  as  a  present  duration  for  sense-aware- 
ness. This  peculiar  relation  is  the  relation  of  cogredi- 
ence between  the  percipient  event  and  the  duration. 


no  THE  CONCEPT  OF  NATURE  [cH. 

Cogredience  is  the  preservation  of  unbroken  quality  of 
standpoint  within  the  duration.  It  is  the  continuance 
of  identity  of  station  within  the  whole  of  nature  which 
is  the  terminus  of  sense-awareness.  The  duration  may 
comprise  change  within  itself,  but  cannot — so  far  as  it 
is  one  present  duration — comprise  change  in  the  quality 
of  its  peculiar  relation  to  the  contained  percipient  event. 

In  other  words,  perception  is  always  'here,*  and  a 
duration  can  only  be  posited  as  present  for  sense-aware- 
ness on  condition  that  it  affords  one  unbroken  meaning 
of  *here'  in  its  relation  to  the  percipient  event.  It  is 
only  in  the  past  that  you  can  have  been  *  there '  with  a 
standpoint  distinct  from  your  present  'here.' 

Events  there  and  events  here  are  facts  of  nature,  and 
the  qualities  of  being  *  there '  and  *  here '  are  not  merely 
qualities  of  awareness  as  a  relation  between  nature  and 
mind.  The  quality  of  determinate  station  in  the  duration 
which  belongs  to  an  event  which  is  *  here '  in  one  deter- 
minate sense  of  'here'  is  the  same  kind  of  quality  of 
station  which  belongs  to  an  event  which  is  'there'  in 
one  determinate  sense  of  'there.'  Thus  cogredience  has 
nothing  to  do  with  any  biological  character  of  the  event 
which  is  related  by  it  to  the  associated  duration.  This 
biological  character  is  apparently  a  further  condition 
for  the  peculiar  connexion  of  a  percipient  event  with 
the  percipience  of  mind ;  but  it  has  nothing  to  do  with 
the  relation  of  the  percipient  event  to  the  duration 
which  is  the  present  whole  of  nature  posited  as  the 
disclosure  of  the  percipience. 

Given  the  requisite  biological  character,  the  event  in 
its  character  of  a  percipient  event  selects  that  duration 
with  which  the  operative  past  of  the  event  is  practi- 
cally cogredient  within  the  limits  of  the  exactitude  of 


V]  SPACE  AND  MOTION  iii 

observation.  Namely,  amid  the  alternative  time-systems 
which  nature  offers  there  will  be  one  with  a  duration 
giving  the  best  average  of  cogredience  for  all  the  sub- 
ordinate parts  of  the  percipient  event.  This  duration 
will  be  the  whole  of  nature  which  is  the  terminus  posited 
by  sense-awareness.  Thus  the  character  of  the  percipient 
event  determines  the  time-system  immediately  evident 
in  nature.  As  the  character  of  the  percipient  event 
changes  with  the  passage  of  nature — or,  in  other  words, 
as  the  percipient  mind  in  its  passage  correlates  itself 
with  the  passage  of  the  percipient  event  into  another 
percipient  event — the  time-system  correlated  with  the 
percipience  of  that  mind  may  change.  When  the  bulk 
of  the  events  perceived  are  cogredient  in  a  duration 
other  than  that  of  the  percipient  event,  the  percipience 
may  include  a  double  consciousness  of  cogredience, 
namely  the  consciousness  of  the  whole  within  which  the 
observer  in  the  train  is  *here,'  and  the  consciousness  of 
the  whole  within  which  the  trees  and  bridges  and 
telegraph  posts  are  definitely  *  there/  Thus  in  per- 
ceptions under  certain  circumstances  the  events  dis- 
criminated assert  their  own  relations  of  cogredience. 
This  assertion  of  cogredience  is  peculiarly  evident  when 
the  duration  to  which  the  perceived  event  is  cogredient 
is  the  same  as  the  duration  which  is  the  present  whole 
of  nature — in  other  words,  when  the  event  and  the  per- 
cipient event  are  both  cogredient  to  the  same  duration. 

We  are  now  prepared  to  consider  the  meaning  of 
stations  in  a  duration,  where  stations  are  a  peculiar 
kind  of  routes,  which  define  absolute  position  in  the 
associated  timeless  space. 

There  are  however  some  preliminary  explanations. 
A  finite  event  will  be  said  to  extend  throughout  a 


112  THE  CONCEPT  OF  NATURE  [ch. 

duration  when  it  is  part  of  the  duration  and  is  inter- 
sected by  any  moment  which  lies  in  the  duration.  Such 
an  event  begins  with  the  duration  and  ends  with  it. 
Furthermore  every  event  which  begins  with  the  dura- 
tion and  ends  with  it,  extends  throughout  the  duration. 
This  is  an  axiom  based  on  the  continuity  of  events.  By 
beginning  with  a  duration  and  ending  with  it,  I  mean 
(i)  that  the  event  is  part  of  the  duration,  and  (ii)  that 
both  the  initial  and  final  boundary  moments  of  the 
duration  cover  some  event-particles  on  the  boundary  of 
the  event. 

Every  event  which  is  cogredient  with  a  duration 
extends  throughout  that  duration. 

It  is  not  true  that  all  the  parts  of  an  event  cogredient 
with  a  duration  are  also  cogredient  with  the  duration. 
The  relation  of  cogredience  may  fail  in  either  of  two 
ways.  One  reason  for  failure  may  be  that  the  part  does 
not  extend  throughout  the  duration.  In  this  case  the 
part  may  be  cogredient  with  another  duration  which  is 
part  of  the  given  duration,  though  it  is  not  cogredient 
with  the  given  duration  itself.  Such  a  part  would  be 
cogredient  if  its  existence  were  sufficiently  prolonged 
in  that  time-system.  The  other  reason  for  failure  arises 
from  the  four-dimensional  extension  of  events  so  that 
there  is  no  determinate  route  of  transition  of  events  in 
linear  series.  For  example,  the  tunnel  of  a  tube  railway 
is  an  event  at  rest  in  a  certain  time-system,  that  is  to  say, 
it  is  cogredient  with  a  certain  duration.  A  train  travel- 
ling in  it  is  part  of  that  tunnel,  but  is  not  itself  at  rest. 

If  an  event  e  be  cogredient  with  a  duration  d,  and 
d!  be  any  duration  which  is  part  of  d.  Then  d'  belongs 
to  the  same  time-system  as  d.  Also  d'  intersects  e  in 
an  event  e'  which  is  part  of  e  and  is  cogredient  with  d' , 


v]  SPACE  AND  MOTION  113 

Let  P  be  any  event-particle  lying  in  a  given  duration 
rf.  Consider  the  aggregate  of  events  in  which  P  lies 
and  which  are  also  cogredient  with  d.  Each  of  these 
events  occupies  its  own  aggregate  of  event-particles. 
These  aggregates  will  have  a  common  portion,  namely 
the  class  of  event-particle  lying  in  all  of  them.  This  class 
of  event-particles  is  what  I  call  the  *  station'  of  the 
event-particle  P  in  the  duration  d.  This  is  the  station  in 
the  character  of  a  locus.  A  station  can  also  be  defined  in 
the  character  of  an  abstractive  element.  Let  the  pro- 
perty o-  be  the  name  of  the  property  which  an  abstractive 
set  possesses  when  (i)  each  of  its  events  is  cogredient 
with  the  duration  d  and  (ii)  the  event-particle  P  lies 
in  each  of  its  events.  Then  the  group  of  (t -primes,  where 
a  has  this  meaning,  is  an  abstractive  element  and  is  the 
station  of  P  in  t/  as  an  abstractive  element.  The  locus 
of  event-particles  covered  by  the  station  oi  P  in  d  as 
an  abstractive  element  is  the  station  of  P  in  rf  as  a 
locus.  A  station  has  accordingly  the  usual  three 
characters,  namely,  its  character  of  position,  its  ex- 
trinsic character  as  an  abstractive  element,  and  its 
intrinsic  character. 

It  follows  from  the  peculiar  properties  of  rest  that 
two  stations  belonging  to  the  same  duration  cannot 
intersect.  Accordingly  every  event-particle  on  a  station 
of  a  duration  has  that  station  as  its  station  in  the  duration. 
Also  every  duration  which  is  part  of  a  given  duration 
intersects  the  stations  of  the  given  duration  in  loci  which 
are  its  own  stations.  By  means  of  these  properties  we  can 
utilise  the  overlappings  of  the  durations  of  one  family — 
that  is,  of  one  time-system — to  prolong  stations  in- 
definitely backwards  and  forwards.  Such  a  prolonged 
station  will  be  called  a  point-track.   A  point-track  is  a 

W.N.  8 


114  THE  CONCEPT  OF  NATURE  [ch. 

locus  of  event-particles.  It  is  defined  by  reference  to 
one  particular  time-system,  a  say.  Corresponding  to 
any  other  time-system  these  will  be  a  different  group 
of  point- tracks.  Every  event-particle  will  lie  on  one 
and  only  one  point-track  of  the  group  belonging  to  any 
one  time-system.  The  group  of  point-tracks  of  the  time- 
system  a  is  the  group  of  points  of  the  timeless  space  of  a . 
Each  such  point  indicates  a  certain  quality  of  absolute 
position  in  reference  to  the  durations  of  the  family 
associated  with  a,  and  thence  in  reference  to  the  suc- 
cessive instantaneous  spaces  lying  in  the  successive 
moments  of  a.  Each  moment  of  a  will  intersect  a 
point-track  in  one  and  only  one  event-particle. 

This  property  of  the  unique  intersection  of  a  moment 
and  a  point-track  is  not  confined  to  the  case  when  the 
moment  and  the  point-track  belong  to  the  same  time- 
system.  Any  two  event-particles  on  a  point-track  are 
sequential,  so  that  they  cannot  lie  in  the  same  moment. 
Accordingly  no  moment  can  intersect  a  point-track 
more  than  once,  and  every  moment  intersects  a  point- 
track  in  one  event-particle. 

Anyone  who  at  the  successive  moments  of  a  should 
be  at  the  event-particles  where  those  moments  intersect 
a  given  point  of  a  will  be  at  rest  in  the  timeless  space 
of  time-system  a.  But  in  any  other  timeless  space 
belonging  to  another  time-system  he  will  be  at  a 
different  point  at  each  succeeding  moment  of  that  time- 
system.  In  other  words  he  will  be  moving.  He  will  be 
moving  in  a  straight  line  with  uniform  velocity.  We 
might  take  this  as  the  definition  of  a  straight  line. 
Namely,  a  straight  line  in  the  space  of  time-system  /3  is 
the  locus  of  those  points  of  jS  which  all  intersect  some 
one  point-track  which  is  a  point  in  the  space  of  some 


V]  SPACE  AND  MOTION  115 

other  time-system.  Thus  each  point  in  the  space  of  a 
time-system  a  is  associated  with  one  and  only  one 
straight  Hne  of  the  space  of  any  other  time-system  ^. 
Furthermore  the  set  of  straight  Hnes  in  space  ^  which 
are  thus  associated  with  points  in  space  a  form  a  com- 
plete family  of  parallel  straight  lines  in  space  j8.  Thus 
there  is  a  one-to-one  correlation  of  points  in  space  a 
with  the  straight  lines  of  a  certain  definite  family  of 
parallel  straight  lines  in  space  )3.  Conversely  there  is 
an  analogous  one-to-one  correlation  of  the  points  in 
space  /3  with  the  straight  lines  of  a  certain  family  of 
parallel  straight  lines  in  space  « .  These  families  will  be 
called  respectively  the  family  of  parallels  in  /3  associated 
with  a,  and  the  family  of  parallels  in  a  associated  with  ^, 
The  direction  in  the  space  of  ^  indicated  by  the  family 
of  parallels  in  /S  will  be  called  the  direction  of  a  in  space 
jS,  and  the  family  of  parallels  in  a  is  the  direction  of  j8 
in  space  a.  Thus  a  being  at  rest  at  a  point  of  space  a 
will  be  moving  uniformly  along  a  line  in  space  j8  which 
is  in  the  direction  of  a  in  space  j8,  and  a  being  at  rest 
at  a  point  of  space  /S  will  be  moving  uniformly  along  a 
line  in  space  a  which  is  in  the  direction  of  jS  in  space  a . 
I  have  been  speaking  of  the  timeless  spaces  which  are 
associated  with  time-systems.  These  are  the  spaces  of 
physical  science  and  of  any  concept  of  space  as  eternal 
and  unchanging.  But  what  we  actually  perceive  is  an 
approximation  to  the  instantaneous  space  indicated  by 
event-particles  which  lie  within  some  moment  of  the 
time-system  associated  with  our  awareness.  The  points 
of  such  an  instantaneous  space  are  event-particles  and 
the  straight  lines  are  rects.  Let  the  time-system  be 
named  a,  and  let  the  moment  of  time-system  a  to 
which  our  quick  perception  of  nature  approximates  be 

8—2 


ii6  THE  CONCEPT  OF  NATURE  [ch. 

called  M.  Any  straight  line  r  in  space  a  is  a  locus  of 
points  and  each  point  is  a  point-track  which  is  a  locus 
of  event-particles.  Thus  in  the  four-dimensional  geo- 
metry of  all  event-particles  there  is  a  two-dimensional 
locus  which  is  the  locus  of  all  event-particles  on  points 
lying  on  the  straight  line  r.  I  will  call  this  locus  of 
event-particles  the  matrix  of  the  straight  line  r.  A 
matrix  intersects  any  moment  in  a  rect.  Thus  the  matrix 
of  r  intersects  the  moment  M  in  a  rect  p .  Thus  p  is  the 
instantaneous  rect  in  M  which  occupies  at  the  moment 
M  the  straight  line  r  in  the  space  of  a.  Accordingly 
when  one  sees  instantaneously  a  moving  being  and  its 
path  ahead  of  it,  what  one  really  sees  is  the  being  at 
some  event-particle  A  lying  in  the  rect  p  which  is  the 
apparent  path  on  the  assumption  of  uniform  motion. 
But  the  actual  rect  p  which  is  a  locus  of  event-particles 
is  never  traversed  by  the  being.  These  event-parti- 
cles are  the  instantaneous  facts  which  pass  with  the 
instantaneous  moment.  What  is  really  traversed  are 
other  event-particles  which  at  succeeding  instants 
occupy  the  same  points  of  space  a  as  those  occupied  by 
the  event-particles  of  the  rect  p.  For  example,  we  see  a 
stretch  of  road  and  a  lorry  moving  along  it.  The  in- 
stantaneously seen  road  is  a  portion  of  the  rect  p — of 
course  only  an  approximation  to  it.  The  lorry  is  the 
moving  object.  But  the  road  as  seen  is  never  traversed. 
It  is  thought  of  as  being  traversed  because  the  intrinsic 
characters  of  the  later  events  are  in  general  so  similar 
to  those  of  the  instantaneous  road  that  we  do  not 
trouble  to  discriminate.  But  suppose  a  land  mine  under 
the  road  has  been  exploded  before  the  lorry  gets  there. 
Then  it  is  fairly  obvious  that  the  lorry  does  not  traverse 
what  we  saw  at  first.    Suppose  the  lorry  is  at  rest  in 


V]  SPACE  AND  MOTION  117 

space  p.  Then  the  straight  line  r  of  space  a  is  in  the 
direction  of  ^  in  space  a,  and  the  rect  p  is  the  repre- 
sentative in  the  moment  M  of  the  Hne  r  of  space  «. 
The  direction  of  p  in  the  instantaneous  space  of  the 
moment  M  is  the  direction  of  jS  in  M,  where  M  is  a 
moment  of  time-system  a.  Again  the  matrix  of  the 
line  r  of  space  a  will  also  be  the  matrix  of  some  line  s 
of  space  /S  which  will  be  in  the  direction  of  a  in  space  j8. 
Thus  if  the  lorry  halts  at  some  point  P  of  space  a  which 
lies  on  the  line  r,  it  is  now  moving  along  the  line  s  of 
space  ^.  This  is  the  theory  of  relative  motion;  the 
common  matrix  is  the  bond  which  connects  the  motion 
of  jS  in  space  a  with  the  motions  of  a  in  space  p. 

Motion  is  essentially  a  relation  between  some  object 
of  nature  and  the  one  timeless  space  of  a  time-system. 
An  instantaneous  space  is  static,  being  related  to  the 
static  nature  at  an  instant.  In  perception  when  we  see 
things  moving  in  an  approximation  to  an  instantaneous 
space,  the  future  lines  of  motion  as  immediately  per- 
ceived are  rects  which  are  never  traversed.  These 
approximate  rects  are  composed  of  small  events,  namely 
approximate  routes  and  event-particles,  which  are 
passed  away  before  the  moving  objects  reach  them. 
Assuming  that  our  forecasts  of  rectilinear  motion  are 
correct,  these  rects  occupy  the  straight  lines  in  timeless 
space  which  are  traversed.  Thus  the  rects  are  symbols 
in  immediate  sense-awareness  of  a  future  which  can 
only  be  expressed  in  terms  of  timeless  space. 

We  are  now  in  a  position  to  explore  the  fundamental 
character  of  perpendicularity.  Consider  the  two  time- 
systems  a  and  p,  each  with  its  own  timeless  space  and 
its  own  family  of  instantaneous  moments  with  their 
instantaneous  spaces.   Let  M  and  A^  be  respectively  a 


128  THE  CONCEPT  OF  NATURE  [ch. 

moment  of  a  and  a  moment  of  jS.  In  M  there  is  the 
direction  of  ^  and  in  A^  there  is  the  direction  of  a. 
But  M  and  A^,  being  moments  of  different  time-systems, 
intersect  in  a  level.  Call  this  level  A.  Then  A  is  an 
instantaneous  plane  in  the  instantaneous  space  of  M 
and  also  in  the  instantaneous  space  of  A^.  It  is  the  locus 
of  all  the  event-particles  which  lie  both  in  M  and  in  A^. 

In  the  instantaneous  space  of  M  the  level  A  is  per- 
pendicular to  the  direction  of  j8  in  M,  and  in  the 
instantaneous  space  of  N  the  level  A  is  perpendicular 
to  the  direction  of  a  in  N,  This  is  the  fundamental 
property  which  forms  the  definition  of  perpendicularity. 
The  symmetry  of  perpendicularity  is  a  particular  in- 
stance of  the  symmetry  of  the  mutual  relations  between 
two  time-systems.  We  shall  find  in  the  next  lecture 
that  it  is  from  this  symmetry  that  the  theory  of  con- 
gruence is  deduced. 

The  theory  of  perpendicularity  in  the  timeless  space 
of  any  time-system  a  follows  immediately  from  this 
theory  of  perpendicularity  in  each  of  its  instantaneous 
spaces.  Let  p  be  any  rect  in  the  moment  M  of  a  and 
let  A  be  a  level  in  M  which  is  perpendicular  to  p .  The 
locus  of  those  points  of  the  space  of  a  which  intersect 
M  in  event-particles  on  p  is  the  straight  line  r  of  space  a , 
and  the  locus  of  those  points  of  the  space  of  a  which 
intersect  M  in  event-particles  on  A  is  the  plane  /  of 
space  a.  Then  the  plane  /  is  perpendicular  to  the  line  r. 

In  this  way  we  have  pointed  out  unique  and  definite 
properties  in  nature  which  correspond  to  perpen- 
dicularity. We  shall  find  that  this  discovery  of  definite 
unique  properties  defining  perpendicularity  is  of 
critical  importance  in  the  theory  of  congruence  which 
is  the  topic  for  the  next  lecture. 


V]  SPACE  AND  MOTION  119 

I  regret  that  it  has  been  necessary  for  me  in  this 
lecture  to  administer  such  a  large  dose  of  four-dimen- 
sional geometry.  I  do  not  apologise,  because  I  am  really 
not  responsible  for  the  fact  that  nature  in  its  most 
fundamental  aspect  is  four-dimensional.  Things  are 
what  they  are ;  and  it  is  useless  to  disguise  the  fact  that 
*  what  things  are '  is  often  very  difficult  for  our  intellects 
to  follow.  It  is  a  mere  evasion  of  the  ultimate  problems 
to  shirk  such  obstacles. 


CHAPTER  VI 

CONGRUENCE 

The  aim  of  this  lecture  is  to  establish  a  theory  of  con- 
gruence. You  must  understand  at  once  that  congruence 
is  a  controversial  question.  It  is  the  theory  of  measure- 
ment in  space  and  in  time.  The  question  seems  simple. 
In  fact  it  is  simple  enough  for  a  standard  procedure  to 
have  been  settled  by  act  of  parliament ;  and  devotion  to 
metaphysical  subtleties  is  almost  the  only  crime  which 
has  never  been  imputed  to  any  English  parliament. 
But  the  procedure  is  one  thing  and  its  meaning  is 
another. 

First  let  us  fix  attention  on  the  purely  mathematical 
question.  When  the  segment  between  two  points  A 
and  B  is  congruent  to  that  between  the  two  points  C 
and  Z),  the  quantitative  measurements  of  the  two  seg- 
ments are  equal.  The  equality  of  the  numerical  measures 
and  the  congruence  of  the  two  segments  are  not  always 
clearly  discriminated,  and  are  lumped  together  under 
the  term  equality.  But  the  procedure  of  measurement 
presupposes  congruence.  For  example,  a  yard  measure 
is  applied  successively  to  measure  two  distances  between 
two  pairs  of  points  on  the  floor  of  a  room.  It  is  of  the 
essence  of  the  procedure  of  measurement  that  the 
yard  measure  remains  unaltered  as  it  is  transferred  from 
one  position  to  another.  Some  objects  can  palpably 
alter  as  they  move — ^for  example,  an  elastic  thread; 
but  a  yard  measure  does  not  alter  if  made  of  the  proper 
material.  What  is  this  but  a  judgment  of  congruence 
applied  to  the  train  of  successive  positions  of  the  yard 


CH.vi]  CONGRUENCE  121 

measure?  We  know  that  it  does  not  alter  because  we 
judge  it  to  be  congruent  to  itself  in  various  positions. 
In  the  case  of  the  thread  we  can  observe  the  loss  of 
self-congruence.  Thus  immediate  judgments  of  con- 
gruence are  presupposed  in  measurement,  and  the 
process  of  measurement  is  merely  a  procedure  to  extend 
the  recognition  of  congruence  to  cases  where  these 
immediate  judgments  are  not  available.  Thus  we  cannot 
define  congruence  by  measurement. 

In  modern  expositions  of  the  axioms  of  geometry 
certain  conditions  are  laid  down  which  the  relation  of 
congruence  between  segments  is  to  satisfy.  It  is 
supposed  that  we  have  a  complete  theory  of  points, 
straight  lines,  planes,  and  the  order  of  points  on  planes — 
in  fact,  a  complete  theory  of  non-metrical  geometry. 
We  then  enquire  about  congruence  and  lay  down  the 
set  of  conditions — or  axioms  as  they  are  called — ^which 
this  relation  satisfies.  It  has  then  been  proved  that 
there  are  alternative  relations  which  satisfy  these  con- 
ditions equally  well  and  that  there  is  nothing  intrinsic 
in  the  theory  of  space  to  lead  us  to  adopt  any  one  of  these 
relations  in  preference  to  any  other  as  the  relation 
of  congruence  which  we  adopt.  In  other  words  there 
are  alternative  metrical  geometries  which  all  exist  by 
an  equal  right  so  far  as  the  intrinsic  theory  of  space  is 
concerned. 

Poincare,  the  great  French  mathematician,  held  that 
our  actual  choice  among  these  geometries  is  guided 
purely  by  convention,  and  that  the  effect  of  a  change  of 
choice  would  be  simply  to  alter  our  expression  of  the 
physical  laws  of  nature.  By  'convention'  I  understand 
Poincare  to  mean  that  there  is  nothing  inherent  in 
nature  itself  giving  any  peculiar  rdle  to  one  of  these 


122  THE  CONCEPT  OF  NATURE  [ch. 

congruence  relations,  and  that  the  choice  of  one  par- 
ticular relation  is  guided  by  the  volitions  of  the  mind  at 
the  other  end  of  the  sense-awareness.  The  principle  of 
guidance  is  intellectual  convenience  and  not  natural 
fact. 

This  position  has  been  misunderstood  by  many  of 
Poincare's  expositors.  They  have  muddled  it  up  with 
another  question,  namely  that  owing  to  the  inexactitude 
of  observation  it  is  impossible  to  make  an  exact  state- 
ment in  the  comparison  of  measures.  It  follows  that  a 
certain  subset  of  closely  allied  congruence  relations  can 
be  assigned  of  which  each  member  equally  well  agrees 
with  that  statement  of  observed  congruence  when  the 
statement  is  properly  qualified  with  its  limits  of 
error. 

This  is  an  entirely  different  question  and  it  pre- 
supposes a  rejection  of  Poincare's  position.  The  absolute 
indetermination  of  nature  in  respect  of  all  the  relations 
of  congruence  is  replaced  by  the  indetermination  of 
observation  with  respect  to  a  small  subgroup  of  these 
relations. 

Poincare's  position  is  a  strong  one.  He  in  effect 
challenges  anyone  to  point  out  any  factor  in  nature 
which  gives  a  preeminent  status  to  the  congruence 
relation  which  mankind  has  actually  adopted.  But  un- 
deniably the  position  is  very  paradoxical.  Bertrand 
Russell  had  a  controversy  with  him  on  this  question, 
and  pointed  out  that  on  Poincare's  principles  there  was 
nothing  in  nature  to  determine  whether  the  earth  is 
larger  or  smaller  than  some  assigned  billiard  ball. 
Poincare  replied  that  the  attempt  to  find  reasons  in 
nature  for  the  selection  of  a  definite  congruence  relation 
in  space  is  like  trying  to  determine  the  position  of  a 


VI]  CONGRUENCE  123 

ship  in  the  ocean  by  counting  the  crew  and  observing 
the  colour  of  the  captain's  eyes. 

In  my  opinion  both  disputants  were  right,  assuming 
the  grounds  on  which  the  discussion  was  based. 
Russell  in  effect  pointed  out  that  apart  from  minor 
inexactitudes  a  determinate  congruence  relation  is 
among  the  factors  in  nature  which  our  sense-awareness 
posits  for  us.  Poincare  asks  for  information  as  to  the 
factor  in  nature  which  might  lead  any  particular  con- 
gruence relation  to  play  a  preeminent  r6le  among  the 
factors  posited  in  sense-awareness.  I  cannot  see  the 
answer  to  either  of  these  contentions  provided  that  you 
admit  the  materialistic  theory  of  nature.  With  this 
heory  nature  at  an  instant  in  space  is  an  independent 
fact.  Thus  we  have  to  look  for  our  preeminent  con- 
gruence relation  amid  nature  in  instantaneous  space; 
and  Poincare  is  undoubtedly  right  in  saying  that  nature 
on  this  hypothesis  gives  us  no  help  in  finding  it. 

On  the  other  hand  Russell  is  in  an  equally  strong 
position  when  he  asserts  that,  as  a  fact  of  observation, 
we  do  find  it,  and  what  is  more  agree  in  finding  the  same 
congruence  relation.  On  this  basis  it  is  one  of  the  most 
extraordinary  facts  of  human  experience  that  all  man- 
kind without  any  assignable  reason  should  agree  in 
fixing  attention  on  just  one  congruence  relation  amid 
the  indefinite  number  of  indistinguishable  competitors 
for  notice.  One  would  have  expected  disagreement  on 
this  fundamental  choice  to  have  divided  nations  and  to 
have  rent  families.  But  the  difficulty  was  not  even  dis- 
covered till  the  close  of  the  nineteenth  century  by  a 
few  mathematical  philosophers  and  philosophic  mathe- 
maticians. The  case  is  not  like  that  of  our  agreement 
on  some  fundamental  fact  of  nature  such  as  the  three 


124  THE  CONCEPT  OF  NATURE  [ch. 

dimensions  of  space.  If  space  has  only  three  dimensions 
we  should  expect  all  mankind  to  be  aware  of  the  fact, 
as  they  are  aware  of  it.  But  in  the  case  of  congruence, 
mankind  agree  in  an  arbitrary  interpretation  of  sense- 
awareness  when  there  is  nothing  in  nature  to  guide  it. 

I  look  on  it  as  no  slight  recommendation  of  the  theory 
of  nature  which  I  am  expounding  to  you  that  it  gives 
a  solution  of  this  difficulty  by  pointing  out  the  factor 
in  nature  which  issues  in  the  preeminence  of  one 
congruence  relation  over  the  indefinite  herd  of  other 
such  relations. 

The  reason  for  this  result  is  that  nature  is  no  longer 
confined  within  space  at  an  instant.  Space  and  time 
are  now  interconnected ;  and  this  peculiar  factor  of  time 
which  is  so  immediately  distinguished  among  the 
deliverances  of  our  sense-awareness,  relates  itself  to 
one  particular  congruence  relation  in  space. 

Congruence  is  a  particular  example  of  the  fundamental 
fact  of  recognition.  In  perception  we  recognise.  This 
recognition  does  not  merely  concern  the  comparison  of 
a  factor  of  nature  posited  by  memory  with  a  factor 
posited  by  immediate  sense-awareness.  Recognition 
takes  place  within  the  present  without  any  intervention 
of  pure  memory.  For  the  present  fact  is  a  duration  with 
its  antecedent  and  consequent  durations  which  are 
parts  of  itself.  The  discrimination  in  sense-awareness 
of  a  finite  event  with  its  quality  of  passage  is  also 
accompanied  by  the  discrimination  of  other  factors  of 
nature  which  do  not  share  in  the  passage  of  events. 
Whatever  passes  is  an  event.  But  we  find  entities  in 
nature  which  do  not  pass ;  namely  we  recognise  same- 
nesses in  nature.  Recognition  is  not  primarily  an 
intellectual  act  of  comparison ;  it  is  in  its  essence  merely 


VI]  CONGRUENCE  125 

sense-awareness  in  its  capacity  of  positing  before  us 
factors  in  nature  which  do  not  pass.  For  example, 
green  is  perceived  as  situated  in  a  certain  finite  event 
within  the  present  duration.  This  green  preserves  its 
self-identity  throughout,  whereas  the  event  passes  and 
thereby  obtains  the  property  of  breaking  into  parts. 
The  green  patch  has  parts.  But  in  talking  of  the  green 
patch  we  are  speaking  of  the  event  in  its  sole  capacity  of 
being  for  us  the  situation  of  green.  The  green  itself  is 
numerically  one  self-identical  entity,  without  parts 
because  it  is  without  passage. 

Factors  in  nature  which  are  without  passage  will  be 
called  objects.  There  are  radically  different  kinds  of  ob- 
jects which  will  be  considered  in  the  succeeding  lecture. 

Recognition  is  reflected  into  the  intellect  as  comparison. 
The  recognised  objects  of  one  event  are  compared  with 
the  recognised  objects  of  another  event.  The  com- 
parison may  be  between  two  events  in  the  present,  or 
it  may  be  between  two  events  of  which  one  is  posited 
by  memory-awareness  and  the  other  by  immediate 
sense-awareness.  But  it  is  not  the  events  which  are 
compared.  For  each  event  is  essentially  unique  and 
incomparable.  What  are  compared  are  the  objects  and 
relations  of  objects  situated  in  events.  The  event  con- 
sidered as  a  relation  between  objects  has  lost  its  passage 
and  in  this  aspect  is  itself  an  object.  This  object  is  not 
the  event  but  only  an  intellectual  abstraction.  The  same 
object  can  be  situated  in  many  events ;  and  in  this  sense 
even  the  whole  event,  viewed  as  an  object,  can  recur, 
though  not  the  very  event  itself  with  its  passage  and  its 
relations  to  other  events. 

Objects  which  are  not  posited  by  sense-awareness 
may  be  known  to  the  intellect.  For  example,  relations 


f' 


^- 


126  THE  CONCEPT  OF  NATURE  [ch. 

between  objects  and  relations  between  relations  may 
be  factors  in  nature  not  disclosed  in  sense-awareness 
but  known  by  logical  inference  as  necessarily  in  being. 
Thus  objects  for  our  knowledge  may  be  merely  logical 
abstractions.  For  example,  a  complete  event  is  never 
disclosed  in  sense-awareness,  and  thus  the  object  which 
is  the  sum  total  of  objects  situated  in  an  event  as  thus 
inter-related  is  a  mere  abstract  concept.  Again  a  right- 
angle  is  a  perceived  object  which  can  be  situated  in 
many  events;  but,  though  rectangularity  is  posited  by 
sense-awareness,  the  majority  of  geometrical  relations 
are  not  so  posited.  Also  rectangularity  is  in  fact  often 
not  perceived  when  it  can  be  proved  to  have  been  there 
for  perception.  Thus  an  object  is  often  known  merely 
as  an  abstract  relation  not  directly  posited  in  sense- 
awareness  although  it  is  there  in  nature. 

The  identity  of  quality  between  congruent  segments 
is  generally  of  this  character.  In  certain  special  cases 
this  identity  of  quality  can  be  directly  perceived.  But 
in  general  it  is  inferred  by  a  process  of  measurement 
depending  on  our  direct  sense-awareness  of  selected 
cases  and  a  logical  inference  from  the  transitive  character 
of  congruence. 

Congruence  depends  on  motion,  and  thereby  is 
generated  the  connexion  between  spatial  congruence 
and  temporal  congruence.  Motion  along  a  straight  line 
has  a  symmetry  round  that  line.  This  symmetry  is  ex- 
pressed by  the  symmetrical  geometrical  relations  of  the 
line  to  the  family  of  planes  normal  to  it. 

Also  another  symmetry  in  the  theory  of  motion  arises 
from  the  fact  that  rest  in  the  points  of  p  corresponds  to 
uniform  motion  along  a  definite  family  of  parallel 
straight  lines  in  the  space  of  a .  We  must  note  the  three 


VI]  CONGRUENCE  127 

characteristics,  (i)  of  the  uniformity  of  the  motion 
corresponding  to  any  point  of  p  along  its  correlated 
straight  line  in  a ,  and  (ii)  of  the  equality  in  magnitude 
of  the  velocities  along  the  various  lines  of  a  correlated 
to  rest  in  the  various  points  of  jS,  and  (iii)  of  the 
parallelism  of  the  lines  of  this  family. 

We  are  nov^  in  possession  of  a  theory  of  parallels  and 
a  theory  of  perpendiculars  and  a  theory  of  motion,  and 
from  these  theories  the  theory  of  congruence  can  be 
constructed.  It  vs^ill  be  remembered  that  a  family  of 
parallel  levels  in  any  moment  is  the  family  of  levels  in 
vs^hich  that  moment  is  intersected  by  the  family  of 
moments  of  some  other  time-system.  Also  a  family  of 
parallel  moments  is  the  family  of  moments  of  some  one 
time-system.  Thus  we  can  enlarge  our  concept  of  a 
family  of  parallel  levels  so  as  to  include  levels  in  diffe- 
rent moments  of  one  time-system.  With  this  enlarged 
concept  vv^e  say  that  a  complete  family  of  parallel  levels 
in  a  time-system  a  is  the  complete  family  of  levels  in 
v^hich  the  moments  of  a  intersect  the  moments  of  j3. 
This  complete  family  of  parallel  levels  is  also  evidently 
a  family  lying  in  the  moments  of  the  time-system  j8. 
By  introducing  a  third  time-system  y,  parallel  rects  are 
obtained.  Also  all  the  points  of  any  one  time-system 
form  a  family  of  parallel  point-tracks.  Thus  there  are 
three  types  of  parallelograms  in  the  four-dimensional 
manifold  of  event-particles. 

In  parallelograms  of  the  first  type  the  two  pairs  of 
parallel  sides  are  both  of  them  pairs  of  rects.  In  parallelo- 
grams of  the  second  type  one  pair  of  parallel  sides 
is  a  pair  of  rects  and  the  other  pair  is  a  pair  of  point- 
tracks.  In  parallelograms  of  the  third  type  the  two  pairs 
of  parallel  sides  are  both  of  them  pairs  of  point-tracks. 


128  THE  CONCEPT  OF  NATURE  [ch. 

The  first  axiom  of  congruence  is  that  the  opposite 
sides  of  any  parallelogram  are  congruent.  This  axiom 
enables  us  to  compare  the  lengths  of  any  two  segments 
either  respectively  on  parallel  rects  or  on  the  same  rect. 
Also  it  enables  us  to  compare  the  lengths  of  any  two  seg- 
ments either  respectively  on  parallel  point-tracks  or  on  the 
same  point-track.  It  follows  from  this  axiom  that  two 
objects  at  rest  in  any  two  points  of  a  time-system  j8  are 
moving  with  equal  velocities  in  any  other  time-system  a 
along  parallel  lines.  Thus  we  can  speak  of  the  velocity 
in  a  due  to  the  time-system  jS  without  specifying  any 
particular  point  in  j3.  The  axiom  also  enables  us  to 
measure  time  in  any  time-system ;  but  does  not  enable 
us  to  compare  times  in  different  time-systems. 

The  second  axiom  of  congruence  concerns  parallelo- 
grams on  congruent  bases  and  between  the  same 
parallels,  which  have  also  their  other  pairs  of  sides 
parallel.  The  axiom  asserts  that  the  rect  joining  the 
two  event-particles  of  intersection  of  the  diagonals  is 
parallel  to  the  rect  on  which  the  bases  lie.  By  the  aid 
of  this  axiom  it  easily  follows  that  the  diagonals  of  a 
parallelogram  bisect  each  other. 

Congruence  is  extended  in  any  space  beyond  parallel 
rects  to  all  rects  by  two  axioms  depending  on  perpen- 
dicularity. The  first  of  these  axioms,  which  is  the  third 
axiom  of  congruence,  is  that  if  ABC  is  a  triangle  of  rects 
in  any  moment  and  D  is  the  middle  event-particle  of  the 
base  BC^  then  the  level  through  2)  perpendicular  to  BC 
contains  A  when  and  only  when  AB  is  congruent  to 
AC,  This  axiom  evidently  expresses  the  symmetry  of 
perpendicularity,  and  is  the  essence  of  the  famous 
pons  asinorum  expressed  as  an  axiom. 

The  second  axiom  depending  on  perpendicularity. 


VI]  CONGRUENCE  129 

and  the  fourth  axiom  of  congruence,  is  that  if  r  and  A 
be  a  rect  and  an  event-particle  in  the  same  moment  and 
AB  and  v^C  be  a  pair  of  rectangular  rects  intersecting 
r  in  5  and  C,  and  AD  and  AE  be  another  pair  of  rect- 
angular rects  intersecting  r  in  Z)  and  £",  then  either  D 
or  E  lies  in  the  segment  BC  and  the  other  one  of  the 
two  does  not  lie  in  this  segment.  Also  as  a  particular 
case  of  this  axiom,  if  AB  be  perpendicular  to  r  and  in 
consequence  ^C  be  parallel  to  r,  then  Z>  and  E  lie  on 
opposite  sides  of  B  respectively.  By  the  aid  of  these 
two  axioms  the  theory  of  congruence  can  be  extended 
so  as  to  compare  lengths  of  segments  on  any  two  rects. 
Accordingly  Euclidean  metrical  geometry  in  space  is 
completely  established  and  lengths  in  the  spaces  of 
different  time-systems  are  comparable  as  the  result  of 
definite  properties  of  nature  which  indicate  just  that 
particular  method  of  comparison. 

The  comparison  of  time-measurements  in  diverse 
time-systems  requires  two  other  axioms.  The  first  of 
these  axioms,  forming  the  fifth  axiom  of  congruence, 
will  be  called  the  axiom  of  *  kinetic  symmetry.'  It 
expresses  the  symmetry  of  the  quantitative  relations 
between  two  time-systems  when  the  times  and  lengths 
in  the  two  systems  are  measured  in  congruent  units. 

The  axiom  can  be  explained  as  follows :  Let  a  and  ^ 
be  the  names  of  two  time-systems.  The  directions  of 
motion  in  the  space  of  a  due  to  rest  in  a  point  of  ^  is 
called  the  *  j8-direction  in  a '  and  the  direction  of  motion 
in  the  space  of  j8  due  to  rest  in  a  point  of  a  is  called  the 
*  a -direction  in  j8.'  Consider  a  motion  in  the  space  of 
a  consisting  of  a  certain  velocity  in  the  jS -direction  of  a 
and  a  certain  velocity  at  right-angles  to  it.  This  motion 
represents  rest  in  the  space  of  another  time-system — 

W.N.  9 


130  THE  CONCEPT  OF  NATURE  [ch. 

call  it  TT .  Rest  in  tt  will  also  be  represented  in  the  space 
of  )S  by  a  certain  velocity  in  the  a -direction  in  /S  and  a 
certain  velocity  at  right-angles  to  this  « -direction.  Thus 
a  certain  motion  in  the  space  of  a  is  correlated  to  a 
certain  motion  in  the  space  of  j8,  as  both  representing 
the  same  fact  which  can  also  be  represented  by  rest  in 
TT.  Now  another  time-system,  which  I  will  name  or, 
can  be  found  which  is  such  that  rest  in  its  space  is 
represented  by  the  same  magnitudes  of  velocities 
along  and  perpendicular  to  the  a -direction  in  j3  as  those 
velocities  in  a,  along  and  perpendicular  to  the  j8 -direc- 
tion, which  represent  rest  in  tt.  The  required  axiom  of 
kinetic  symmetry  is  that  rest  in  a  will  be  represented  in 
a  by  the  same  velocities  along  and  perpendicular  to 
the  j3 -direction  in  a  as  those  velocities  in  /3  along  and 
perpendicular  to  the  a -direction  which  represent  rest 
in  TT. 

A  particular  case  of  this  axiom  is  that  relative  velocities 
are  equal  and  opposite.  Namely  rest  in  a  is  represented 
in  j3  by  a  velocity  along  the  a -direction  which  is  equal 
to  the  velocity  along  the  ^S -direction  in  a  which  repre- 
sents rest  in  j3. 

Finally  the  sixth  axiom  of  congruence  is  that  the 
relation  of  congruence  is  transitive.  So  far  as  this 
axiom  applies  to  space,  it  is  superfluous.  For  the 
property  follows  from  our  previous  axioms.  It  is 
however  necessary  for  time  as  a  supplement  to  the  axiom 
of  kinetic  symmetry.  The  meaning  of  the  axiom  is  that 
if  the  time-unit  of  system  a  is  congruent  to  the  time- 
unit  of  system  ^,  and  the  time-unit  of  system  ^  is 
congruent  to  the  time-unit  of  system  y,  then  the  time- 
units  of  a  and  y  are  also  congruent. 

By  means  of  these  axioms  formulae  for  the  trans- 


VI]  CONGRUENCE  131 

formation  of  measurements  made  in  one  time-system 
to  measurements  of  the  same  facts  of  nature  made  in 
another  time-system  can  be  deduced.  These  formulae 
will  be  found  to  involve  one  arbitrary  constant  vy^hich 
I  v^ill  call  k. 

It  is  of  the  dimensions  of  the  square  of  a  velocity. 
Accordingly  four  cases  arise.  In  the  first  case  k  is 
zero.  This  case  produces  nonsensical  results  in  opposi- 
tion to  the  elementary  deliverances  of  experience.  We 
put  this  case  aside. 

In  the  second  case  k  is  infinite.  This  case  yields  the 
ordinary  formulae  for  transformation  in  relative  motion, 
namely  those  formulae  v^hich  are  to  be  found  in  every 
elementary  book  on  dynamics. 

In  the  third  case,  k  is  negative.  Let  us  call  it  —  c^, 
where  c  will  be  of  the  dimensions  of  a  velocity.  This 
case  yields  the  formulae  of  transformation  which 
Larmor  discovered  for  the  transformation  of  Maxwell's 
equations  of  the  electromagnetic  field.  These  formulae 
were  extended  by  H.  A.  Lorentz,  and  used  by  Einstein 
and  Minkowski  as  the  basis  of  their  novel  theory  of 
relativity.  I  am  not  now  speaking  of  Einstein's  more 
recent  theory  of  general  relativity  by  which  he  deduces 
his  modification  of  the  law  of  gravitation.  If  this  be  the 
case  which  applies  to  nature,  then  c  must  be  a  close 
approximation  to  the  velocity  of  light  in  vacuo.  Perhaps 
it  is  this  actual  velocity.  In  this  connexion  ^in  vacuo' 
must  not  mean  an  absence  of  events,  namely  the  absence 
of  the  all-pervading  ether  of  events.  It  must  mean  the 
absence  of  certain  types  of  objects. 

In  the  fourth  case,  k  is  positive.  Let  us  call  it  A^, 
where  A  will  be  of  the  dimensions  of  a  velocity.  This  gives 
a  perfectly  possible  type  of  transformation  formulae, 

9—2 


132  THE  CONCEPT  OF  NATURE  [ch. 

but  not  one  which  explains  any  facts  of  experience. 
It  has  also  another  disadvantage.  With  the  assumption 
of  this  fourth  case  the  distinction  between  space  and 
time  becomes  unduly  blurred.  The  whole  object  of 
these  lectures  has  been  to  enforce  the  doctrine  that 
space  and  time  spring  from  a  common  root,  and  that 
the  ultimate  fact  of  experience  is  a  space-time  fact.  But 
after  all  mankind  does  distinguish  very  sharply  between 
space  and  time,  and  it  is  owing  to  this  sharpness  of 
distinction  that  the  doctrine  of  these  lectures  is  some- 
what of  a  paradox.  Now  in  the  third  assumption  this 
sharpness  of  distinction  is  adequately  preserved.  There 
is  a  fundamental  distinction  between  the  metrical  pro- 
perties of  point-tracks  and  rects.  But  in  the  fourth 
assumption  this  fundamental  distinction  vanishes. 

Neither  the  third  nor  the  fourth  assumption  can 
agree  with  experience  unless  we  assume  that  the 
velocity  c  of  the  third  assumption,  and  the  velocity  h 
of  the  fourth  assumption,  are  extremely  large  compared 
to  the  velocities  of  ordinary  experience.  If  this  be  the 
case  the  formulae  of  both  assumptions  will  obviously 
reduce  to  a  close  approximation  to  the  formulae  of  the 
second  assumption  which  are  the  ordinary  formulae  of 
dynamical  textbooks.  For  the  sake  of  a  name,  I  will 
call  these  textbook  formulae  the  *  orthodox'  formulae. 

There  can  be  no  question  as  to  the  general  approxi- 
mate correctness  of  the  orthodox  formulae.  It  would  be 
merely  silly  to  raise  doubts  on  this  point.  But  the 
determination  of  the  status  of  these  formulae  is  by  no 
means  settled  by  this  admission.  The  independence 
of  time  and  space  is  an  unquestioned  presupposition 
of  the  orthodox  thought  which  has  produced  the  ortho- 
dox formulae.   With  this  presupposition  and  given  the 


VI]  CONGRUENCE  133 

absolute  points  of  one  absolute  space,  the  orthodox 
formulae  are  immediate  deductions.  Accordingly, 
these  formulae  are  presented  to  our  imaginations  as 
facts  which  cannot  be  otherwise,  time  and  space  being 
what  they  are.  The  orthodox  formulae  have  therefore 
attained  to  the  status  of  necessities  which  cannot  be 
questioned  in  science.  Any  attempt  to  replace  these 
formulae  by  others  was  to  abandon  the  rdle  of  physical 
explanation  and  to  have  recourse  to  mere  mathematical 
formulae. 

But  even  in  physical  science  difficulties  have  accumu- 
lated round  the  orthodox  formulae.  In  the  first  place 
Maxwell's  equations  of  the  electromagnetic  field  are 
not  invariant  for  the  transformations  of  the  orthodox 
formulae;  whereas  they  are  invariant  for  the  trans- 
formations of  the  formulae  arising  from  the  third  of  the 
four  cases  mentioned  above,  provided  that  the  velocity  c 
is  identified  with  a  famous  electromagnetic  constant 
quantity. 

Again  the  null  results  of  the  delicate  experiments 
to  detect  the  earth's  variations  of  motion  through  the 
ether  in  its  orbital  path  are  explained  immediately  by 
the  formulae  of  the  third  case.  But  if  we  assume  the 
orthodox  formulae  we  have  to  make  a  special  and  ar- 
bitrary assumption  as  to  the  contraction  of  matter  during 
motion.   I  mean  the  Fitzgerald-Lorentz  assumption. 

Lastly  Fresnel's  coefficient  of  drag  which  represents 
the  variation  of  the  velocity  of  light  in  a  moving  medium 
is  explained  by  the  formulae  of  the  third  case,  and 
requires  another  arbitrary  assumption  if  we  use  the 
orthodox  formulae. 

It  appears  therefore  that  on  the  mere  basis  of 
physical  explanation  there  are  advantages  in  the  formulae 


134  THE  CONCEPT  OF  NATURE  [ch. 

of  the  third  case  as  compared  with  the  orthodox  for- 
mulae. But  the  way  is  blocked  by  the  ingrained  belief 
that  these  latter  formulae  possess  a  character  of  necessity. 
It  is  therefore  an  urgent  requisite  for  physical  science 
and  for  philosophy  to  examine  critically  the  grounds 
for  this  supposed  necessity.  The  only  satisfactory 
method  of  scrutiny  is  to  recur  to  the  first  principles  of 
our  knowledge  of  nature.  This  is  exactly  what  I  am 
endeavouring  to  do  in  these  lectures.  I  ask  what  it  is 
that  we  are  aware  of  in  our  sense-perception  of  nature. 
I  then  proceed  to  examine  those  factors  in  nature  which 
lead  us  to  conceive  nature  as  occupying  space  and 
persisting  through  time.  This  procedure  has  led  us  to 
an  investigation  of  the  characters  of  space  and  time.  It 
results  from  these  investigations  that  the  formulae  of 
the  third  case  and  the  orthodox  formulae  are  on  a  level 
as  possible  formulae  resulting  from  the  basic  character 
of  our  knowledge  of  nature.  The  orthodox  formulae 
have  thus  lost  any  advantage  as  to  necessity  which  they 
enjoyed  over  the  serial  group.  The  way  is  thus  open  to 
adopt  whichever  of  the  two  groups  best  accords  with 
observation. 

I  take  this  opportunity  of  pausing  for  a  moment  from 
the  course  of  my  argument,  and  of  reflecting  on  the 
general  character  which  my  doctrine  ascribes  to  some 
familiar  concepts  of  science.  I  have  no  doubt  that  some 
of  you  have  felt  that  in  certain  aspects  this  character 
is  very  paradoxical. 

This  vein  of  paradox  is  partly  due  to  the  fact  that 
educated  language  has  been  made  to  conform  to  the 
prevalent  orthodox  theory.  We  are  thus,  in  expounding 
an  alternative  doctrine,  driven  to  the  use  of  either  strange 
terms  or  of  familiar  words  with  unusual  meanings.  This 


VI]  CONGRUENCE  135 


victory  of  the  orthodox  theory  over  language  is  very       /JjP 


natural.  Events  are  named  after  the  prominent  objects 
situated  in  them,  and  thus  both  in  language  and  in 
thought  the  event  sinks  behind  the  object,  and  becomes 
the  mere  play  of  its  relations.  The  theory  of  space  is 
then  converted  into  a  theory  of  the  relations  of  objects 
instead  of  a  theory  of  the  relations  of  events.  But  objects 
have  not  the  passage  of  events.  Accordingly  space  as  a 
relation  between  objects  is  devoid  of  any  connexion 
with  time.  It  is  space  at  an  instant  without  any  deter- 
minate relations  between  the  spaces  at  successive  in- 
stants. It  cannot  be  one  timeless  space  because  the 
relations  between  objects  change. 

A  few  minutes  ago  in  speaking  of  the  deduction  of 
the  orthodox  formulae  for  relative  motion  I  said  that 
they  followed  as  an  immediate  deduction  from  the 
assumption  of  absolute  points  in  absolute  space.  This 
reference  to  absolute  space  was  not  an  oversight.  I  know 
that  the  doctrine  of  the  relativity  of  space  at  present 
holds  the  field  both  in  science  and  philosophy.  But 
I  do  not  think  that  its  inevitable  consequences  are 
understood.  When  we  really  face  them  the  paradox  of 
the  presentation  of  the  character  of  space  which  I  have 
elaborated  is  greatly  mitigated.  If  there  is  no  absolute 
position,  a  point  must  cease  to  be  a  simple  entity.  What 
is  a  point  to  one  man  in  a  balloon  with  his  eyes  fixed  on 
an  instrument  is  a  track  of  points  to  an  observer  on  the 
earth  who  is  watching  the  balloon  through  a  telescope, 
and  is  another  track  of  points  to  an  observer  in  the  sun 
who  is  watching  the  balloon  through  some  instrument 
suited  to  such  a  being.  Accordingly  if  I  am  reproached 
with  the  paradox  of  my  theory  of  points  as  classes  of 
event-particles,  and  of  my  theory  of  event-particles  as 


u' 


■A 


136  THE  CONCEPT  OF  NATURE  [ch. 

groups  of  abstractive  sets,  I  ask  my  critic  to  explain 
exactly  what  he  means  by  a  point.  While  you  explain 
your  meaning  about  anything,  however  simple,  it  is 
always  apt  to  look  subtle  and  fine  spun.  I  have  at  least 
explained  exactly  what  I  do  mean  by  a  point,  what 
relations  it  involves  and  what  entities  are  the  relata. 
If  you  admit  the  relativity  of  space,  you  also  must 
admit  that  points  are  complex  entities,  logical  constructs 
involving  other  entities  and  their  relations.  Produce 
your  theory,  not  in  a  few  vague  phrases  of  indefinite 
meaning,  but  explain  it  step  by  step  in  definite  terms 
referring  to  assigned  relations  and  assigned  relata.  Also 
show  that  your  theory  of  points  issues  in  a  theory  of 
space.  Furthermore  note  that  the  example  of  the  man 
in  the  balloon,  the  observer  on  earth,  and  the  observer 
in  the  sun,  shows  that  every  assumption  of  relative  rest 
requires  a  timeless  space  with  radically  different  points 
from  those  which  issue  from  every  other  such  assump- 
tion. The  theory  of  the  relativity  of  space  is  incon- 
sistent with  any  doctrine  of  one  unique  set  of  points  of 
one  timeless  space. 

The  fact  is  that  there  is  no  paradox  in  my  doctrine 
of  the  nature  of  space  which  is  not  in  essence  inherent 
in  the  theory  of  the  relativity  of  space.  But  this  doctrine 
has  never  really  been  accepted  in  science,  whatever 
people  say.  What  appears  in  our  dynamical  treatises  is 
Newton's  doctrine  of  relative  motion  based  on  the 
doctrine  of  differential  motion  in  absolute  space.  When 
you  once  admit  that  the  points  are  radically  different 
entities  for  differing  assumptions  of  rest,  then  the 
orthodox  formulae  lose  all  their  obviousness.  They 
were  only  obvious  because  you  were  really  thinking  of 
something  else.    When  discussing  this  topic  you  can 


VI]  CONGRUENCE  137 

only  avoid  paradox  by  taking  refuge  from  the  flood  of 
criticism  in  the  comfortable  ark  of  no  meaning. 

The  nev^  theory  provides  a  definition  of  the  con- 
gruence of  periods  of  time.  The  prevalent  viev^  pro- 
vides no  such  definition.  Its  position  is  that  if  we 
take  such  time-measurements  so  that  certain  familiar 
velocities  which  seem  to  us  to  be  uniform  are  uniform, 
then  the  laws  of  motion  are  true.  Now  in  the  first  place 
no  change  could  appear  either  as  uniform  or  non- 
uniform without  involving  a  definite  determination  of 
the  congruence  for  time-periods.  So  in  appealing  to 
familiar  phenomena  it  allows  that  there  is  some 
factor  in  nature  which  we  can  intellectually  construct 
as  a  congruence  theory.  It  does  not  however  say  any- 
thing about  it  except  that  the  laws  of  motion  are  then 
true.  Suppose  that  with  some  expositors  we  cut  out 
the  reference  to  familiar  velocities  such  as  the  rate  of 
rotation  of  the  earth.  We  are  then  driven  to  admit  that 
there  is  no  meaning  in  temporal  congruence  except 
that  certain  assumptions  make  the  laws  of  motion  true. 
Such  a  statement  is  historically  false.  King  Alfred  the 
Great  was  ignorant  of  the  laws  of  motion,  but  knew 
very  well  what  he  meant  by  the  measurement  of  time, 
and  achieved  his  purpose  by  means  of  burning  candles. 
Also  no  one  in  past  ages  justified  the  use  of  sand  in 
hour-glasses  by  saying  that  some  centuries  later  in- 
teresting laws  of  motion  would  be  discovered  which 
would  give  a  meaning  to  the  statement  that  the  sand 
was  emptied  from  the  bulbs  in  equal  times.  Uniformity  i 
in  change  is  directly  perceived,  and  it  follows  that 
mankind  perceives  in  nature  factors  from  which  a  theory 
of  temporal  congruence  can  be  formed.  The  prevalent 
theory  entirely  fails  to  produce  such  factors. 


138  THE  CONCEPT  OF  NATURE  [ch. 

The  mention  of  the  laws  of  motion  raises  another 
point  where  the  prevalent  theory  has  nothing  to  say 
and  the  new  theory  gives  a  complete  explanation.  It  is 
well  known  that  the  laws  of  motion  are  not  valid  for 
any  axes  of  reference  which  you  may  choose  to  take 
fixed  in  any  rigid  body.  You  must  choose  a  body  which 
is  not  rotating  and  has  no  acceleration.  For  example 
they  do  not  really  apply  to  axes  fixed  in  the  earth 
because  of  the  diurnal  rotation  of  that  body.  The  law 
which  fails  when  you  assume  the  wrong  axes  as  at  rest 
is  the  third  law,  that  action  and  reaction  are  equal  and 
opposite.  With  the  wrong  axes  uncompensated  centri- 
fugal forces  and  uncompensated  composite  centrifugal 
forces  appear,  due  to  rotation.  The  influence  of  these 
forces  can  be  demonstrated  by  many  facts  on  the  earth's 
surface,  Foucault's  pendulum,  the  shape  of  the  earth, 
the  fixed  directions  of  the  rotations  of  cyclones  and 
anticyclones.  It  is  difficult  to  take  seriously  the  sug- 
gestion that  these  domestic  phenomena  on  the  earth 
are  due  to  the  influence  of  the  fixed  stars.  I  cannot 
persuade  myself  to  believe  that  a  little  star  in  its 
twinkling  turned  round  Foucault's  pendulum  in  the 
Paris  Exhibition  of  186 1.  Of  course  anything  is  believ- 
able when  a  definite  physical  connexion  has  been 
demonstrated,  for  example  the  influence  of  sunspots. 
Here  all  demonstration  is  lacking  in  the  form  of  any 
coherent  theory.  According  to  the  theory  of  these 
lectures  the  axes  to  which  motion  is  to  be  referred  are 
axes  at  rest  in  the  space  of  some  time-system.  For 
example,  consider  the  space  of  a  time-system  a.  There 
are  sets  of  axes  at  rest  in  the  space  of  a .  These  are  suitable 
dynamical  axes.  Also  a  set  of  axes  in  this  space  which 
is  moving  with  uniform  velocity  without  rotation  is 


VI]  CONGRUENCE  139 

another  suitable  set.  All  the  moving  points  fixed  in 
these  moving  axes  are  really  tracing  out  parallel  lines 
with  one  uniform  velocity.  In  other  words  they  are 
the  reflections  in  the  space  of  a  of  a  set  of  fixed  axes  in 
the  space  of  some  other  time-system  jS.  Accordingly 
the  group  of  dynamical  axes  required  for  Newton's 
Laws  of  Motion  is  the  outcome  of  the  necessity  of 
referring  motion  to  a  body  at  rest  in  the  space  of  some 
one  time-system  in  order  to  obtain  a  coherent  account 
of  physical  properties.  If  we  do  not  do  so  the  meaning 
of  the  motion  of  one  portion  of  our  physical  configuration 
is  different  from  the  meaning  of  the  motion  of  another 
portion  of  the  same  configuration.  Thus  the  meaning 
of  motion  being  what  it  is,  in  order  to  describe  the  motion 
of  any  system  of  objects  without  changing  the  meaning 
of  your  terms  as  you  proceed  vdth  your  description, 
you  are  bound  to  take  one  of  these  sets  of  axes  as  axes 
of  reference ;  though  you  may  choose  their  reflections 
into  the  space  of  any  time-system  which  you  wish  to 
adopt.  A  definite  physical  reason  is  thereby  assigned  for 
the  peculiar  property  of  the  dynamical  group  of  axes. 

On  the  orthodox  theory  the  position  of  the  equations 
of  motion  is  most  ambiguous.  The  space  to  which  they 
refer  is  completely  undetermined  and  so  is  the  measure- 
ment of  the  lapse  of  time.  Science  is  simply  setting  out 
on  a  fishing  expedition  to  see  whether  it  cannot  find 
some  procedure  which  it  can  call  the  measurement  of 
space  and  some  procedure  which  it  can  call  the  measure- 
ment of  time,  and  something  which  it  can  call  a  system 
of  forces,  and  something  which  it  can  call  masses,  so 
that  these  formulae  may  be  satisfied.  The  only  reason — 
on  this  theory — ^why  anyone  should  want  to  satisfy 
these  formulae  is  a  sentimental  regard  for  Galileo, 


140  THE  CONCEPT  OF  NATURE  [ch. 

Newton,  Euler  and  Lagrange.  The  theory,  so  far  from 
founding  science  on  a  sound  observational  basis,  forces 
everything  to  conform  to  a  mere  mathematical  pre- 
ference for  certain  simple  formulae. 

I  do  not  for  a  moment  believe  that  this  is  a  true  ac- 
count of  the  real  status  of  the  Laws  of  Motion.  These 
equations  want  some  slight  adjustment  for  the  new 
formulae  of  relativity.  But  with  these  adjustments, 
imperceptible  in  ordinary  use,  the  laws  deal  with  funda- 
mental physical  quantities  which  we  know  very  well 
and  wish  to  correlate. 

The  measurement  of  time  was  known  to  all  civilised 
nations  long  before  the  laws  were  thought  of.  It  is  this 
time  as  thus  measured  that  the  laws  are  concerned  with. 
Also  they  deal  with  the  space  of  our  daily  life.  When  we 
approach  to  an  accuracy  of  measurement  beyond  that 
of  observation,  adjustment  is  allowable.  But  within  the 
limits  of  observation  we  know  what  we  mean  when  we 
speak  of  measurements  of  space  and  measurements  of 
time  and  uniformity  of  change.  It  is  for  science  to  give  an 
intellectual  account  of  what  is  so  evident  in  sense-aware- 
ness. It  is  to  me  thoroughly  incredible  that  the  ultimate 
fact  beyond  which  there  is  no  deeper  explanation  is  that 
mankind  has  really  been  swayed  by  an  unconscious 
desire  to  satisfy  the  mathematical  formulae  which  we 
call  the  Laws  of  Motion,  formulae  completely  unknown 
till  the  seventeenth  century  of  our  epoch. 

The  correlation  of  the  facts  of  sense-experience 
effected  by  the  alternative  account  of  nature  extends 
beyond  the  physical  properties  of  motion  and  the 
properties  of  congruence.  It  gives  an  account  of  the 
meaning  of  the  geometrical  entities  such  as  points, 
straight  lines,  and  volumes,  and  connects  the  kindred 


VI]  CONGRUENCE  141 

ideas  of  extension  in  time  and  extension  in  space.  The 
theory  satisfies  the  true  purpose  of  an  intellectual 
explanation  in  the  sphere  of  natural  philosophy.  This 
purpose  is  to  exhibit  the  interconnexions  of  nature,  and 
to  show  that  one  set  of  ingredients  in  nature  requires 
for  the  exhibition  of  its  character  the  presence  of  the 
other  sets  of  ingredients. 

The  false  idea  which  we  have  to  get  rid  of  is  that  of 
nature  as  a  mere  aggregate  of  independent  entities,  each 
capable  of  isolation.  According  to  this  conception  these 
entities,  whose  characters  are  capable  of  isolated  defini- 
tion, come  together  and  by  their  accidental  relations 
form  the  system  of  nature.  This  system  is  thus  thoroughly 
accidental;  and,  even  if  it  be  subject  to  a  mechanical 
fate,  it  is  only  accidentally  so  subject. 

With  this  theory  space  might  be  without  time,  and 
time  might  be  without  space.  The  theory  admittedly 
breaks  down  when  we  come  to  the  relations  of  matter 
and  space.  The  relational  theory  of  space  is  an  admission 
that  we  cannot  know  space  without  matter  or  matter 
without  space.  But  the  seclusion  of  both  from  time  is 
still  jealously  guarded.  The  relations  between  portions 
of  matter  in  space  are  accidental  facts  owing  to  the 
absence  of  any  coherent  account  of  how  space  springs 
from  matter  or  how  matter  springs  from  space.  Also 
what  we  really  observe  in  nature,  its  colours  and  its 
sounds  and  its  touches  are  secondary  qualities;  in 
other  words,  they  are  not  in  nature  at  all  but  are  acci- 
dental products  of  the  relations  between  nature  and 
mind. 

The  explanation  of  nature  which  I  urge  as  an  alter- 
native ideal  to  this  accidental  view  of  nature,  is  that 
nothing  in  nature  could  be  what  it  is  except  as  an 


142  THE  CONCEPT  OF  NATURE  [ch.  vi 

ingredient  in  nature  as  it  is.  The  whole  which  is  present 
for  discrimination  is  posited  in  sense-awareness  as 
necessary  for  the  discriminated  parts.  An  isolated  event 
is  not  an  event,  because  every  event  is  a  factor  in  a 
larger  whole  and  is  significant  of  that  whole.  There  can 
be  no  time  apart  from  space ;  and  no  space  apart  from 
time ;  and  no  space  and  no  time  apart  from  the  passage 
of  the  events  of  nature.  The  isolation  of  an  entity  in 
thought,  when  we  think  of  it  as  a  bare  *it,'  has  no 
counterpart  in  any  corresponding  isolation  in  nature. 
Such  isolation  is  merely  part  of  the  procedure  of  intel- 
lectual knowledge. 

The  laws  of  nature  are  the  outcome  of  the  characters 
of  the  entities  which  we  find  in  nature.  The  entities 
being  what  they  are,  the  laws  must  be  what  they  are; 
and  conversely  the  entities  follow  from  the  laws.  We 
are  a  long  way  from  the  attainment  of  such  an  ideal; 
but  it  remains  as  the  abiding  goal  of  theoretical  science. 


CHAPTER  VII 

OBJECTS 

The  ensuing  lecture  is  concerned  with  the  theory  of 
objects.  Objects  are  elements  in  nature  which  do  not 
pass.  The  awareness  of  an  object  as  some  factor  not 
sharing  in  the  passage  of  nature  is  what  I  call  *recogni-| 
tion.'  Itis^inpossibleJ:o  recognise  an^event^  because 
an  event  is  essentially  distinct  from  every  other  event. 
Recognition  is  an  awareness  of  samenessj  But  to  call 
recognition  an  awareness  of  sameness  implies  an  in- 
tellectual act  of  comparison  accompanied  with  judgment. 
I  use  recognition  for  the  non-intellectual  relation  of 
sense-awareness  which  connects  the  mind  with  a  factor 
of  nature  without  passage.  On  the  intellectual  side  of 
the  mind's  experience  there  are  comparisons  of  things 
recognised  and  consequent  judgments  of  sameness  or 
diversity.  Probably  *  sense-recognition '  would  be  a 
better  term  for  what  I  mean  by  *  recognition.'  I  have 
chosen  the  simpler  term  because  I  think  that  I  shall  be 
able  to  avoid  the  use  of  *  recognition '  in  any  other 
meaning  than  that  of  *  sense-recognition.'  I  am  quite 
willing  to  believe  that  recognition,  in  my  sense  of  the 
term,  is  merely  an  ideal  limit,  and  that  there  is  in  fact 
no  recognition  without  intellectual  accompaniments  of 
comparison  and  judgment.  But  recognition  is  that 
relation  of  the  mind  to  nature  which  provides  the 
material  for  the  intellectual  activity. 

An  object  is  an  ingredient  in  the  character  of  some 
event.  In  fact  the  character  of  an  event  is  nothing  but 
the  objects  which  are  ingredient  in  it  and  the  ways  in 


144  THE  CONCEPT  OF  NATURE  [ch. 

(which  those  objects  make  their  ingression  into  the 
event.  Thus  the  theory  of  objects  is  the  theory  of  the 
comparison  of  events.  Events  are  only  comparable 
because  they  body  forth  permanences.  We  are  com- 
paring objects  in  events  whenever  we  can  say,  *  There 
it  is  again.'  Objects  are  the  elements  in  nature  which 
can  *be  again.' 

Sometimes  permanences  can  be  proved  to  exist 
which  evade  recognition  in  the  sense  in  which  I  am 
using  that  term.  The  permanences  which  evade  recogni- 
tion appear  to  us  as  abstract  properties  either  of  events 
or  of  objects.  All  the  same  they  are  there  for  recognition 
although  undiscriminated  in  our  sense-awareness.  The 
demarcation  of  events,  the  splitting  of  nature  up  into 
parts  is  effected  by  the  objects  which  we  recognise  as 
their  ingredients.  The  discrimination  of  nature  is  the 
recognition  of  objects  amid  passing  events.  It  is  a 
compound  of  the  awareness  of  the  passage  of  nature, 
of  the  consequent  partition  of  nature,  and  of  the  defini- 
tion of  certain  parts  of  nature  by  the  modes  of  the 
ingression  of  objects  into  them. 

You  may  have  noticed  that  I  am  using  the  term 
*  ingression'  to  denote  the  general  relation  of  objects 
to  events.  The  ingression  of  an  object  into  an  event  is 
the  way  the  character  of  the  event  shapes  itself  in  virtue 
of  the  being  of  the  object.  Namely  the  event  is  what  it 
is,  because  the  object  is  what  it  is ;  and  when  I  am  thinking 
of  this  modification  of  the  event  by  the  object,  I  call 
the  relation  between  the  two  *the  ingression  of  the 
object  into  the  event.'  It  is  equally  true  to  say  that 
objects  are  what  they  are  because  events  are  what  they 

iare.  Nature  is  such  that  there  can  be  no  events  and  no 
objects  without  the  ingression  of  objects  into  events. 


VII]  OBJECTS  145 

Although  there  are  events  such  that  the  ingredient! 
objects  evade  our  recognition.  These  are  the  events  in( 
empty  space.  Such  events  are  only  analysed  for  us  by]| 
the  intellectual  probing  of  science. 

Ingression  is  a  relation  vv^hich  has  various  modes. 
There  are  obviously  very  various  kinds  of  objects; 
and  no  one  kind  of  object  can  have  the  same  sort  of 
relations  to  events  as  objects  of  another  kind  can  have. 
We  shall  have  to  analyse  out  some  of  the  different 
modes  of  ingression  w^hich  different  kinds  of  objects 
have  into  events. 

But  even  if  wt  stick  to  one  and  the  same  kind  of 
objects,  an  object  of  that  kind  has  different  modes  of 
ingression  into  different  events.    Science  and  philo- 
sophy have  been  apt  to  entangle  themselves  in  a  simple- 
minded  theory  that  an  object  is  at  one  place  at  any  definite 
time,  and  is  in  no  sense  anyvs^here  else.  This  is  in  fact 
the  attitude  of  common  sense  thought,  though  it  is  not 
the  attitude  of  language  vv^hich  is  naively  expressing  the 
facts  oFexperience.  Every  other  sentence  in  a  w^ork  of 
literature  which  is  endeavouring  truly  to  interpret  the 
facts  of  experience  expresses  differences  in  surrounding 
events  due  to  the  presence  of  some  object.   An  object 
is  ingredient  throughout  its  neighbourhood,  and  its 
neighbourhood  is  indefinite.   Also  the  modification  of 
events    by   ingression   is    susceptible    of   quantitative 
differences.    Finally  therefore  we  are  driven  to  admit  / 
that  each  object  is  in  some  sense  ingredient  throughout  I 
nature;  though   its  ingression  may  be  quantitatively  ' 
irrelevant  in  the  expression  of  our  individual  experi- 
ences. 

This  admission  is  not  new  either  in  philosophy  or 
science.    It  is  obviously  a  necessary  axiom  for  those 

W.N.  10 


146  THE  CONCEPT  OF  NATURE  [ch. 

philosophers  who  insist  that  reahty  is  a  system.  In 
these  lectures  we  are  keeping  off  the  profound  and 
vexed  question  as  to  what  we  mean  by  *reaUty.'  I  am 
maintaining  the  humbler  thesis  that  nature  is  a  system. 
But  I  suppose  that  in  this  case  the  less  follows  from 
the  greater,  and  that  I  may  claim  the  support  of  these 
philosophers.  The  same  doctrine  is  essentially  interwoven 
in  all  modern  physical  speculation.  As  long  ago  as  1847 
Faraday  in  a  paper  in  the  Philosophical  Magazine 
remarked  that  his  theory  of  tubes  of  force  im.plies  that 
in  a  sense  an  electric  charge  is  everywhere.  The  modi- 
fication of  the  electromagnetic  field  at  every  point  of 
space  at  each  instant  owing  to  the  past  history  of  each 
electron  is  another  way  of  stating  the  same  fact.  We 
can  however  illustrate  the  doctrine  by  the  more  familiar 
facts  of  life  without  recourse  to  the  abstruse  speculations 
of  theoretical  physics. 

The  waves  as  they  roll  on  to  the  Cornish  coast  tell 
of  a  gale  in  mid-Atlantic ;  and  our  dinner  witnesses  to 
the-ingression  of  the  cook  into  the  dining  room.  It  is 
'  evident  that  the  ingression  of  objects  into  events  in- 
cludes the  theory  of  causation.  I  prefer  to  neglect  this 
aspect  of  ingression,  because  causation  raises  the 
memory  of  discussions  based  upon  theories  of  nature 
which  are  alien  to  my  own.  Also  I  think  that  some  new 
light  may  be  thrown  on  the  subject  by  viewing  it  in 
this  fresh  aspect. 

The  examples  which  I  have  given  of  the  ingression 
of  objects  into  events  remind  us  that  ingression  takes 
a  peculiar  form  in  the  case  of  some  events;  in  a  sense, 
it  is  a  more  concentrated  form.  For  example,  the  electron 
has  a  certain  position  in  space  and  a  certain  shape. 
Perhaps  it  is  an  extremely  small  sphere  in  a  certain 


VII]  OBJECTS  147 

test-tube.  The  storm  is  a  gale  situated  in  mid- Atlantic 
with  a  certain  latitude  and  longitude,  and  the  cook  is  in 
the  kitchen.  I  will  call  this  special  form  of  ingression 
the  'relation  of  situation';  also,  by  a  double  use  of  the 
word  *  situation,'  I  will  call  the  event  in  which  an  object 
is  situated  *  the  situation  of  the  object.'  Thus  a  situation 
is  an  event  which  is  a  relatum  in  the  relation  of  situation. 
Now  our  first  impression  is  that  at  last  we  have  come  to 
the  simple  plain  fact  of  where  the  object  really  is ;  and 
that  the  vaguer  relation  which  I  call  ingression  should 
not  be  muddled  up  with  the  relation  of  situation,  as  if 
including  it  as  a  particular  case.  It  seems  so  obvious 
that  any  object  is  in  such  and  such  a  position,  and  that 
it  is  influencing  other  events  in  a  totally  different  sense. 
Namely,  in  a  sense  an  object  is  the  character  of  the 
event  which  is  its  situation,  but  it  onlv  influences  the 
character  of  other  events.  Accordingly  the  relations  of 
situation  and  influencing  are  not  generally  the  same  sort 
of  relation,  and  should  not  be  subsumed  under  the  same 
term '  ingression.'  I  believe  that  this  notion  is  a  mistake, 
and  that  it  is  impossible  to  draw  a  clear  distinction 
between  the  two  relations. 

For  example.  Where  was  your  toothache?  You  went 
to  a  dentist  and  pointed  out  the  tooth  to  him.  He  pro- 
nounced it  perfectly  sound,  and  cured  you  by  stopping 
another  tooth.  Which  tooth  was  the  situation  of  the 
toothache?  Again,  a  man  has  an  arm  amputated,  and 
experiences  sensations  in  the  hand  which  he  has  lost. 
The  situation  of  the  imaginary  hand  is  in  fact  merely 
thin  air.  You  look  into  a  mirror  and  see  a  fire.  The  flames 
that  you  see  are  situated  behind  the  mirror.  Again  at 
night  you  watch  the  sky ;  if  some  of  the  stars  had  vanished 
from  existence  hours  ago,  you  would  not  be  any  the 

10 — 2 


148  THE  CONCEPT  OF  NATURE  [ch. 

wiser.  Even  the  situations  of  the  planets  differ  from 
those  which  science  would  assign  to  them. 

Anyhow  you  are  tempted  to  exclaim,  the  cook  is  in 
the  kitchen.  If  you  mean  her  mind,  I  will  not  agree 
with  you  on  the  point;  for  I  am  only  talking  of  nature. 
Let  us  think  only  of  her  bodily  presence.  What  do  you 
mean  by  this  notion?  We  confine  ourselves  to  typical 
manifestations  of  it.  You  can  see  her,  touch  her,  and 
hear  her.  But  the  examples  which  I  have  given  you 
show  that  the  notions  of  the  situations  of  what  you  see, 
what  you  touch,  and  what  you  hear  are  not  so  sharply 
separated  out  as  to  defy  further  questioning.  You 
cannot  cling  to  the  idea  that  we  have  two  sets  of  ex- 
periences of  nature,  one  of  primary  qualities  which 
belong  to  the  objects  perceived,  and  one  of  secondary 
qualities  which  are  the  products  of  our  mental  excite- 
ments. All  we  know  of  nature  is  in  the  same  boat,  to 
sink  or  swim  together.  The  constructions  of  science 
are  merely  expositions  of  the  characters  of  things  per- 
ceived. Accordingly  to  affirm  that  the  cook  is  a  certain 
dance  of  molecules  and  electrons  is  merely  to  affirm 
that  the  things  about  her  which  are  perceivable  have 
certain  characters.  The  situations  of  the  perceived 
manifestations  of  her  bodily  presence  have  only  a  very 
general  relation  to  the  situations  of  the  molecules,  to 
be  determined  by  discussion  of  the  circumstances  of 
perception. 

In  discussing  the  relations  of  situation  in  particular 
and  of  ingression  in  general,  the  first  requisite  is  to  note 
that  objects  are  of  radically  different  types.  For  each 
type  '  situation '  and  '  ingression '  have  their  own  special 
meanings  which  are  different  from  their  meanings  for 
other  types,  though  connexions  can  be  pointed  out. 


VII]  OBJECTS  149 

It  is  necessary  therefore  in  discussing  them  to  deter- 
mine what  type  of  objects  are  under  consideration. 
There  are,  I  think,  an  indefinite  number  of  types  of 
objects.  Happily  we  need  not  think  of  them  all.  The  ) 
idea  of  situation  has  its  peculiar  importance  in  reference 
to  three  types  of  objects  which  I  call  sense-objects, 
perceptual  objects  and  scientific  objects.  The  suitability 
of  these  names  for  the  three  types  is  of  minor  import- 
ance, so  long  as  I  can  succeed  in  explaining  what  I  mean 
by  them. 

These  three  types  form  an  ascending  hierarchy,  of 
which  each  member  presupposes  the  type  below.  Thel 
base  of  the  hierarchy  is  formed  by  the  sense-objects. 
These  objects  do  not  presuppose  any  other  type  of 
objects.  A  sense-object  is  a  factor  of  nature  posited  | 
by  sense-awareness  which  (i),  in  that  it  is  an  object,  does  I 
not  share  in  the  passage  of  nature  and  (ii)  is  not  a  J 
relation  between  other  factors  of  nature.  It  will  of 
course  be  a  relatum  in  relations  which  also  implicate 
other  factors  of  nature.  But  it  is  always  a  relatum  and 
never  the  relation  itself.  Examples  of  sense-objects  are 
a  particular  sort  of  colour,  say  Cambridge  blue,  or  a 
particular  sort  of  sound,  or  a  particular  sort  of  smell, 
or  a  particular  sort  of  feeling.  I  am  not  talking  of  a 
particular  patch  of  blue  as  seen  during  a  particular 
second  of  time  at  a  definite  date.  Such  a  patch  is  an 
event  where  Cambridge  blue  is  situated.  Similarly  I  am 
not  talking  of  any  particular  concert-room  as  filled  with 
the  note.  I  mean  the  note  itself  and  not  the  patch  of 
volume  filled  by  the  sound  for  a  tenth  of  a  second.  It  is 
natural  for  us  to  think  of  the  note  in  itself,  but  in  the 
case  of  colour  we  are  apt  to  think  of  it  merely  as  a 
property  of  the  patch.   No  one  thinks  of  the  note  as  a 


150  THE  CONCEPT  OF  NATURE  [ch. 

property  of  the  concert-room.  We  see  the  blue  and  we 
hear  the  note.  Both  the  blue  and  the  note  are  im- 
mediately posited  by  the  discrimination  of  sense-aware- 
ness which  relates  the  mind  to  nature.  The  blue  is 
posited  as  in  nature  related  to  other  factors  in  nature. 
In  particular  it  is  posited  as  in  the  relation  of  being 
situated  in  the  event  which  is  its  situation. 

The  difficulties  which  cluster  around  the  relation  of 
situation  arise  from  the  obstinate  refusal  of  philosophers 
to  take  seriously  the  ultimate  fact  of  multiple  relations. 
By  a  multiple  relation  I  mean  a  relation  which  in  any 
concrete  instance  of  its  occurrence  necessarily  involves 
more  than  two  relata.  For  example,  when  John  likes 
Thomas  there  are  only  two  relata,  John  and  Thomas. 
But  when  John  gives  that  book  to  Thomas  there  are 
three  relata,  John,  that  book,  and  Thomas. 

Some  schools  of  philosophy,  under  the  influence  of 
the  Aristotelian  logic  and  the  Aristotelian  philosophy, 
endeavour  to  get  on  without  admitting  any  relations  at 
all  except  that  of  substance  and  attribute.  Namely  all 
apparent  relations  are  to  be  resolvable  into  the  con- 
current existence  of  substances  with  contrasted  at- 
tributes. It  is  fairly  obvious  that  the  Leibnizian  monad- 
ology  is  the  necessary  outcome  of  any  such  philosophy. 
If  you  dislike  pluralism,  there  will  be  only  one  monad. 

Other  schools  of  philosophy  admit  relations  but 
obstinately  refuse  to  contemplate  relations  with  more 
than  two  relata.  I  do  not  think  that  this  limitation  is 
based  on  any  set  purpose  or  theory.  It  merely  arises 
from  the  fact  that  more  complicated  relations  are  a 
bother  to  people  without  adequate  mathematical  training, 
when  they  are  admitted  into  the  reasoning. 

I  must  repeat  that  we  have  nothing  to  do  in  these 


VII]  OBJECTS  151 

lectures  with  the  ultimate  character  of  reality.  It  is 
quite  possible  that  in  the  true  philosophy  of  reality 
there  are  only  individual  substances  with  attributes, 
or  that  there  are  only  relations  with  pairs  of  relata.  I  do 
not  believe  that  such  is  the  case ;  but  I  am  not  concerned 
to  argue  about  it  now.  Our  theme  is  Nature.  So  long 
as  we  confine  ourselves  to  the  factors  posited  in  the 
sense-awareness  of  nature,  it  seems  to  me  that  there 
certainly  are  instances  of  multiple  relations  between 
these  factors,  and  that  the  relation  of  situation  for  sense- 
objects  is  one  example  of  such  multiple  relations. 

Consider  a  blue  coat,  a  flannel  coat  of  Cambridge 
blue  belonging  to  some  athlete.  The  coat  itself  is  a 
perceptual  object  and  its  situation  is  not  what  I  am 
talking  about.  We  are  talking  of  someone's  definite 
sense-awareness  of  Cambridge  blue  as  situated  in  some 
event  of  nature.  He  may  be  looking  at  the  coat  directly. 
He  then  sees  Cambridge  blue  as  situated  practically  in  the 
same  event  as  the  coat  at  that  instant.  It  is  true  that  the 
blue  which  he  sees  is  due  to  light  which  left  the  coat 
some  inconceivably  small  fraction  of  a  second  before. 
This  diflFerence  would  be  important  if  he  were  looking  at 
a  starwhosecolourwas  Cambridge  blue.  The  star  might 
have  ceased  to  exist  days  ago,  or  even  years  ago.  The 
situation  of  the  blue  will  not  then  be  very  intimately 
connected  with  the  situation  (in  another  sense  of 
*  situation ')  of  any  perceptual  object.  This  disconnexion 
of  the  situation  of  the  blue  and  the  situation  of  some 
associated  perceptual  object  does  not  require  a  star  for 
its  exemplification.  Any  looking  glass  will  suffice.  Look 
at  the  coat  through  a  looking  glass.  Then  blue  is  seen 
as  situated  behind  the  mirror.  The  event  which  is  its 
situation  depends  upon  the  position  of  the  observer. 


152  THE  CONCEPT  OF  NATURE  [ch. 

The  sense-awareness  of  the  blue  as  situated  in  a 
certain  event  which  I  call  the  situation,  is  thus  ex- 
hibited as  the  sense-awareness  of  a  relation  between  the 
blue,  the  percipient  event  of  the  observer,  the  situation, 
and  intervening  events.  All  nature  is  in  fact  required, 
though  only  certain  intervening  events  require  their 
characters  to  be  of  certain  definite  sorts.  The  ingression 
of  blue  into  the  events  of  nature  is  thus  exhibited  as 
systematically  correlated.  The  awareness  of  the  observer 
depends  on  the  position  of  the  percipient  event  in  this 
systematic  correlation.  I  will  use  the  term  'ingression 
into  nature '  for  this  systematic  correlation  of  the  blue 
with  nature.  Thus  the  ingression  of  blue  into  any  definite 
event  is  a  part  statement  of  the  fact  of  the  ingression 
of  blue  into  nature. 

In  respect  to  the  ingression  of  blue  into  nature  events 
may  be  roughly  put  into  four  classes  which  overlap  and 
are  not  very  clearly  separated.  These  classes  are  (i)  the 
percipient  events,  (ii)  the  situations,  (iii)  the  active 
conditioning  events,  (iv)  the  passive  conditioning  events. 
To  understand  this  classification  of  events  in  the  general 
fact  of  the  ingression  of  blue  into  nature,  let  us  confine 
attention  to  one  situation  for  one  percipient  event  and 
to  the  consequent  roles  of  the  conditioning  events  for 
the  ingression  as  thus  limited.  The  percipient  event  is 
the  relevant  bodily  state  of  the  observer.  The  situation 
is  where  he  sees  the  blue,  say,  behind  the  mirror.  The 
active  conditioning  events  are  the  events  whose  charac- 
ters are  particularly  relevant  for  the  event  (which  is  the 
situation)  to  be  the  situation  for  that  percipient  event, 
namely  the  coat,  the  mirror,  and  the  state  of  the  room 
as  to  light  and  atmosphere.  The  passive  conditioning 
events  are  the  events  of  the  rest  of  nature. 


VII]  OBJECTS  153 

In  general  the  situation  is  an  active  conditioning 
event;  namely  the  coat  itself,  when  there  is  no  mirror 
or  other  such  contrivance  to  produce  abnormal  effects. 
But  the  example  of  the  mirror  shows  us  that  the  situation 
may  be  one  of  the  passive  conditioning  events.  We  are 
then  apt  to  say  that  our  senses  have  been  cheated, 
because  we  demand  as  a  right  that  the  situation  should 
be  an  active  condition  in  the  ingression. 

This  demand  is  not  so  baseless  as  it  may  seem  when 
presented  as  I  have  put  it.  All  we  know  of  the  characters 
of  the  events  of  nature  is  based  on  the  analysis  of  the 
relations  of  situations  to  percipient  events.  If  situations 
were  not  in  general  active  conditions,  this  analysis 
would  tell  us  nothing.  Nature  would  be  an  unfathom- 
able enigma  to  us  and  there  could  be  no  science.  Ac- 
cordingly the  incipient  discontent  when  a  situation  is 
found  to  be  a  passive  condition  is  in  a  sense  justifiable ; 
because  if  that  sort  of  thing  went  on  too  often,  the  rdle 
of  the  intellect  would  be  ended. 

Furthermore  the  mirror  is  itself  the  situation  of  other 
sense-objects  either  for  the  same  observer  with  the 
same  percipient  event,  or  for  other  observers  with 
other  percipient  events.  Thus  the  fact  that  an  event  is  a 
situation  in  the  ingression  of  one  set  of  sense-objects 
into  nature  is  presumptive  evidence  that  that  event  is 
an  active  condition  in  the  ingression  of  other  sense- 
objects  into  nature  which  may  have  other  situations. 

This  is  a  fundamental  principle  of  science  which  it  has 
derived  from  common  sense. 

I  now  turn  to  perceptual  objects.  When  we  look  at 
the  coat,  we  do  not  in  general  say.  There  is  a  patch  of 
Cambridge  blue ;  what  naturally  occurs  to  us  is,  There 
is  a  coat.  Also  the  judgment  that  what  we  have  seen  is 


154  THE  CONCEPT  OF  NATURE  [ch 

a  garment  of  man's  attire  is  a  detail.  What  we  perceive 
is  an  object  other  than  a  mere  sense-object.  It  is  not  a 
mere  patch  of  colour,  but  something  more;  and  it  is 
that  something  more  which  we  judge  to  be  a  coat.  I 
will  use  the  word  *coat'  as  the  name  for  that  crude 
object  which  is  more  than  a  patch  of  colour,  and  without 
any  allusion  to  the  judgments  as  to  its  usefulness  as  an 
»  article  of  attire  either  in  the  past  or  the  future.  The  coat 
which  is  perceived — in  this  sense  of  the  word  '  coat  * — 
is  what  I  call  a  perceptual  object.  We  have  to  investigate 
the  general  character  of  these  perceptual  objects. 

It  is  a  law  of  nature  that  in  general  the  situation  of  a 
sense-object  is  not  only  the  situation  of  that  sense- 
object  for  one  definite  percipient  event,  but  is  the 
situation  of  a  variety  of  sense-objects  for  a  variety  of 
percipient  events.  For  example,  for  any  one  percipient 
event,  the  situation  of  a  sense-object  of  sight  is  apt  also 
to  be  the  situations  of  sense-objects  of  sight,  of  touch, 
of  smell,  and  of  sound.  Furthermore  this  concurrence 
in  the  situations  of  sense-objects  has  led  to  the  body — 
i£,  the  percipient  event — so  adapting  itself  that  the 
perception  of  one  sense-object  in  a  certain  situation 
leads  to  a  subconscious  sense-awareness  of  other  sense- 
objects  in  the  same  situation.  This  interplay  is  especially 
the  case  between  touch  and  sight.  There  is  a  certain 
correlation  between  the  ingressions  of  sense-objects 
of  touch  and  sense-objects  of  sight  into  nature,  and  in  a 
slighter  degree  between  the  ingressions  of  other  pairs 
of  sense-objects.  I  call  this  sort  of  correlation  the  *  con- 
veyance' of  one  sense-object  by  another.  When  you 
see  the  blue  flannel  coat  you  subconsciously  feel  yourself 
wearing  it  or  otherwise  touching  it.  If  you  are  a 
smoker,  you  may  also  subconsciously  be  aware  of  the 


VII]  OBJECTS  155 

faint  aroma  of  tobacco.  The  peculiar  fact,  posited  by 
this  sense-awareness  of  the  concurrence  of  subconscious 
sense-objects  along  with  one  or  more  dominating  sense- 
objects  in  the  same  situation,  is  the  sense-awareness  of 
the  perceptual  object.  The  perceptual  object  is  not  1 
primarily  the  issue  of  a  judgment.  It  is  a  factor  of  nature  j    u-fi 
directly  posited  in  sense-awareness.  The  element  of  L,  -- — 
judgment  comes  in  when  we  proceed  to  classify  thej;^ 
particular  perceptual  object.    For  example,  we  say,  - 
That  is  flannel,  and  we  think  of  the  properties  of  flannel 
and  the  uses  of  athletes'  coats.  But  that  all  takes  place 
after  we  have  got  hold  of  the  perceptual  object.  Anti- 
cipatory judgments  affect  the  perceptual  object  per- 
ceived by  focussing  and  diverting  attention. 

The  perceptual  object  is  the  outcome  of  the  habit  of 
experience.  Anything  which  conflicts  with  this  habit 
hinders  the  sense-awareness  of  such  an  object.  A  sense- 
object  is  not  the  product  of  the  association  of  intellectual 
ideas ;  it  is  the  product  of  the  association  of  sense-objects 
in  the  same  situation.  This  outcome  is  not  intellectual; 
it  is  an  object  of  peculiar  type  with  its  own  particular 
ingression  into  nature. 

There  are  two  kinds  of  perceptual  objects,  namely, 
'delusive  perceptual  objects'  and  *  physical  objects.' 
The  situation  of  a  delusive  perceptual  object  is  a 
passive  condition  in  the  ingression  of  that  object  into 
nature.  Also  the  event  which  is  the  situation  will  have 
the  relation  of  situation  to  the  object  only  for  one 
particular  percipient  event.  For  example,  an  observer 
sees  the  image  of  the  blue  coat  in  a  mirror.  It  is  a  blue 
coat  that  he  sees  and  not  a  mere  patch  of  colour.  This 
shows  that  the  active  conditions  for  the  conveyance 
of  a  group  of  subconscious  sense-objects  by  a  dominating 


,^^^^ 


156  THE  CONCEPT  OF  NATURE  [CH. 

sense-object  are  to  be  found  in  the  percipient  event. 
Namely  we  are  to  look  for  them  in  the  investigations 
of  medical  psychologists.  The  ingression  into  nature  of 
the  delusive  sense-object  is  conditioned  by  the  adapta- 
tion of  bodily  events  to  the  more  normal  occurrence, 
which  is  the  ingression  of  the  physical  object. 

A  perceptual  object  is  a  physical  object  when  (i)  its 
situation  is  an  active  conditioning  event  for  the  in- 
gression of  any  of  its  component  sense-objects,  and 
(ii)  the  same  event  can  be  the  situation  of  the  perceptual 
object  for  an  indefinite  number  of  possible  percipient 
events.  Physical  objects  are  the  ordinary  objects  which 
we  perceive  when  our  senses  are  not  cheated,  such  as 
chairs,  tables  and  trees.  In  a  way  physical  objects  have 
more  insistent  perceptive  power  than  sense-objects. 
Attention  to  the  fact  of  their  occurrence  in  nature  is  the 
first  condition  for  the  survival  of  complex  living  or- 
ganisms. The  result  of  this  high  perceptive  power  of 
physical  objects  is  the  scholastic  philosophy  of  nature 
which  looks  on  the  sense-objects  as  mere  attributes  of 
the  physical  objects.  This  scholastic  point  of  view  is 
directly  contradicted  by  the  wealth  of  sense-objects 
which  enter  into  our  experience  as  situated  in  events 
without  any  connexion  with  physical  objects.  For 
example,  stray  smells,  sounds,  colours  and  more  subtle 
nameless  sense-objects.  There  is  no  perception  of 
physical  objects  without  perception  of  sense-objects. 
But  the  converse  does  not  hold:  namely,  there  is 
abundant  perception  of  sense-objects  unaccompanied 
by  any  perception  of  physical  objects.  This  lack  of 
reciprocity  in  the  relations  between  sense-objects  and 
physical  objects  is  fatal  to  the  scholastic  natural  philo- 
sophy. 


VII]  OBJECTS  157 

There  is  a  great  difference  in  the  rSles  of  the  situa- 
tions of  sense-objects  and  physical  objects.  The  situa- 
tions of  a  physical  object  are  conditioned  by  uniqueness 
and  continuity.  The  uniqueness  is  an  ideal  limit  to 
which  we  approximate  as  we  proceed  in  thought  along 
an  abstractive  set  of  durations,  considering  smaller 
and  smaller  durations  in  the  approach  to  the  ideal  limit 
of  the  moment  of  time.  In  other  words,  when  the 
duration  is  small  enough,  the  situation  of  the  physical 
object  within  that  duration  is  practically  unique. 

The  identification  of  the  same  physical  object  as 
being  situated  in  distinct  events  in  distinct  durations  is 
effected  by  the  condition  of  continuity.  This  condition 
of  continuity  is  the  condition  that  a  continuity  of  passage 
of  events,  each  event  being  a  situation  of  the  object  in 
its  corresponding  duration,  can  be  found  from  the  earlier 
to  the  later  of  the  two  given  events.  So  far  as  the  two 
events  are  practically  adjacent  in  one  specious  present, 
this  continuity  of  passage  may  be  directly  perceived. 
Otherwise  it  is  a  matter  of  judgment  and  inference. 

The  situations  of  a  sense-object  are  not  conditioned 
by  any  such  conditions  either  of  uniqueness  or  of  con- 
tinuity. In  any  durations  however  small  a  sense-object 
may  have  any  number  of  situations  separated  from  each 
other.  Thus  two  situations  of  a  sense-object,  either  in 
the  same  duration  or  in  different  durations,  are  not 
necessarily  connected  by  any  continuous  passage  of 
events  which  are  also  situations  of  that  sense-object. 

The  characters  of  the  conditioning  events  involved  in 
the  ingression  of  a  sense-object  into  nature  can  be 
largely  expressed  in  terms  of  the  physical  objects  which 
are  situated  in  those  events.  In  one  respect  this  is  also 
a  tautology.  For  the  physical  object  is  nothing  else  than 


158  THE  CONCEPT  OF  NATURE  [ch. 

the  habitual  concurrence  of  a  certain  set  of  sense-objects 
in  one  situation.  Accordingly  when  we  know  all  about 
the  physical  object,  we  thereby  know  its  component 
sense-objects.  But  a  physical  object  is  a  condition  for 
the  occurrence  of  sense-objects  other  than  those  which 
are  its  components.  For  example,  the  atmosphere  causes 
the  events  which  are  its  situations  to  be  active  con- 
ditioning events  in  the  transmission  of  sound.  A  mirror 
which  is  itself  a  physical  object  is  an  active  condition  for 
the  situation  of  a  patch  of  colour  behind  it,  due  to  the 
reflection  of  light  in  it. 

""  Thus  the  origin  of  scientific  knowledge  is  the  en- 
deavour to  express  in  terms  of  physical  objects  the 
various  r6les  of  events  as  active  conditions  in  the  in- 
gression  of  sense-objects  into  nature.  It  is  in  the  progress 
of  this  investigation  that  scientific  objects  emerge.  They 
embody  those  aspects  of  the  character  of  the  situations 
of  the  physical  objects  which  are  most  permanent  and 
are  expressible  without  reference  to  a  multiple  relation 
including  a  percipient  event.  Their  relations  to  each 
other  are  also  characterised  by  a  certain  simplicity  and 
uniformity.  Finally  the  characters  of  the  observed 
physical  objects  and  sense-objects  can  be  expressed  in 
terms  of  these  scientific  objects.  In  fact  the  whole 
point  of  the  search  for  scientific  objects  is  the  endeavour 
to  obtain  this  simple  expression  of  the  characters  of 
events.  These  scientific  objects  are  not  themselves 
merely  formulae  for  calculation ;  because  formulae  must 
refer  to  things  in  nature,  and  the  scientific  objects  are 
the  things  in  nature  to  which  the  formulae  refer. 

A  scientific  object  such  as  a  definite  electron  is  a 
systematic  correlation  of  the  characters  of  all  events 
throughout  all  nature.   It  is  an  aspect  of  the  systematic 


VII]  OBJECTS  159 

character  of  nature.  The  electron  is  not  merely  where 
its  charge  is.  The  charge  is  the  quantitative  character 
of  certain  events  due  to  the  ingression  of  the  electron 
into  nature.  The  electron  is  its  whole  field  of  force. 
Namely  the  electron  is  the  systematic  way  in  which  all 
events  are  modified  as  the  expression  of  its  ingression. 
The  situation  of  an  electron  in  any  small  duration  may 
be  defined  as  that  event  which  has  the  quantitative 
character  which  is  the  charge  of  the  electron.  We  may 
if  we  please  term  the  mere  charge  the  electron.  But 
then  another  name  is  required  for  the  scientific  object 
which  is  the  full  entity  which  concerns  science,  and 
which  I  have  called  the  electron. 

According  to  this  conception  of  scientific  objects,  the 
rival  theories  of  action  at  a  distance  and  action  by 
transmission  through  a  medium  are  both  incomplete 
expressions  of  the  true  process  of  nature.  The  stream 
of  events  which  form  the  continuous  series  of  situations 
of  the  electron  is  entirely  self-determined,  both  as 
regards  having  the  intrinsic  character  of  being  the  series 
of  situations  of  that  electron  and  as  regards  the  time- 
systems  with  which  its  various  members  are  cogredient, 
and  the  flux  of  their  positions  in  their  corresponding 
durations.  This  is  the  foundation  of  the  denial  of  action 
at  a  distance ;  namely  the  progress  of  the  stream  of  the 
situations  of  a  scientific  object  can  be  determined  by  an 
analysis  of  the  stream  itself. 

On  the  other  hand  the  ingression  of  every  electron 
into  nature  modifies  to  some  extent  the  character  of 
every  event.  Thus  the  character  of  the  stream  of  events 
which  we  are  considering  bears  marks  of  the  existence 
of  every  other  electron  throughout  the  universe.  If  we 
like  to  think  of  the  electrons  as  being  merely  what  I  call 


i6o  THE  CONCEPT  OF  NATURE  [ch. 

their  charges,  then  the  charges  act  at  a  distance.  But 
this  action  consists  in  the  modification  of  the  situation 
of  the  other  electron  under  consideration.  This  con- 
ception of  a  charge  acting  at  a  distance  is  a  wholly 
artificial  one.  The  conception  which  most  fully  expresses 
the  character  of  nature  is  that  of  each  event  as  modified 
by  the  ingression  of  each  electron  into  nature.  The  ether 
is  the  expression  of  this  systematic  modification  of  events 
throughout  space  and  throughout  time.  The  best  expres- 
sion of  the  character  of  this  modification  is  for  physicists 
to  find  out.  My  theory  has  nothing  to  do  with  that  and 
is  ready  to  accept  any  outcome  of  physical  research. 

The  connexion  of  objects  with  space  requires  eluci- 
dation. Objects  are  situated  in  events.  The  relation  of 
situation  is  a  different  relation  for  each  type  of  object, 
and  in  the  case  of  sense-objects  it  cannot  be  expressed 
as  a  two-termed  relation.  It  would  perhaps  be  better 
to  use  a  different  word  for  these  different  types  of  the 
relation  of  situation.  It  has  not  however  been  necessary 
to  do  so  for  our  purposes  in  these  lectures.  It  must  be 
understood  however  that,  when  situation  is  spoken  of, 
some  one  definite  type  is  under  discussion,  and  it  may 
happen  that  the  argument  may  not  apply  to  situation  of 
another  type.  In  all  cases  however  I  use  situation  to 
express  a  relation  between  objects  and  events  and  not 
between  objects  and  abstractive  elements.  There  is  a 
derivative  relation  between  objects  and  spatial  elements 
which  I  call  the  relation  of  location;  and  when  this 
relation  holds,  I  say  that  the  object  is  located  in  the 
abstractive  element.  In  this  sense,  an  object  may  be 
located  in  a  moment  of  time,  in  a  volume  of  space,  an 
area,  a  line,  or  a  point.  There  will  be  a  peculiar  type  of 
location  corresponding  to  each  type  of  situation;  and 


VII]  OBJECTS  i6i 

location  is  in  each  case  derivative  from  the  corresponding 
relation  of  situation  in  a  v^ay  w^hich  I  v^ill  proceed  to 
explain. 

Also  location  in  the  timeless  space  of  some  time-system 
is  a  relation  derivative  from  location  in  instantaneous 
spaces  of  the  same  time-system.  Accordingly  location 
in  an  instantaneous  space  is  the  primary  idea  w^hich  w^e 
have  to  explain.  Great  confusion  has  been  occasioned 
in  natural  philosophy  by  the  neglect  to  distinguish  be- 
tw^een  the  different  types  of  objects,  the  different  types 
of  situation,  the  different  types  of  location,  and  the 
difference  betw^een  location  and  situation.  It  is  im- 
possible to  reason  accurately  in  the  vague  concerning 
objects  and  their  positions  vs^ithout  keeping  these  dis- 
tinctions in  viev^.  An  object  is  located  in  an  abstractive 
element,  when  an  abstractive  set  belonging  to  that  ele- 
ment can  be  found  such  that  each  event  belonging  to 
that  set  is  a  situation  of  the  object.  It  v^ill  be  remem- 
bered that  an  abstractive  element  is  a  certain  group  of 
abstractive  sets,  and  that  each  abstractive  set  is  a  set 
of  events.  This  definition  defines  the  location  of  an 
element  in  any  type  of  abstractive  element.  In  this 
sense  v^e  can  talk  of  the  existence  of  an  object  at  an 
instant,  meaning  thereby  its  location  in  some  definite 
moment.  It  may  also  be  located  in  some  spatial  element 
of  the  instantaneous  space  of  that  moment. 

A  quantity  can  be  said  to  be  located  in  an  abstractive 
element  vv^hen  an  abstractive  set  belonging  to  the  element 
can  be  found  such  that  the  quantitative  expressions  of 
the  corresponding  characters  of  its  events  converge  to 
the  measure  of  the  given  quantity  as  a  limit  v^hen  we 
pass  along  the  abstractive  set  towards  its  converging 
end. 

W.N.  II 


i62  THE  CONCEPT  OF  NATURE  [ch. 

By  these  definitions  location  in  elements  of  instanta- 
neous spaces  is  defined.  These  elements  occupy  corre- 
sponding elements  of  timeless  spaces.  An  object  located 
in  an  element  of  an  instantaneous  space  will  also  be  said 
to  be  located  at  that  moment  in  the  timeless  element  of 
the  timeless  space  which  is  occupied  by  that  instantaneous 
element. 

It  is  not  every  object  which  can  be  located  in  a  moment. 
An  object  which  can  be  located  in  every  moment  of  some 
duration  will  be  called  a  *  uniform'  object  throughout 
that  duration.  Ordinary  physical  objects  appear  to  us 
to  be  uniform  objects,  and  we  habitually  assume  that 
scientific  objects  such  as  electrons  are  uniform.  But 
some  sense-objects  certainly  are  not  uniform.  A  tune 
is  an  example  of  a  non-uniform  object.  We  have  per- 
ceived it  as  a  whole  in  a  certain  duration ;  but  the  tune 
as  a  tune  is  not  at  any  moment  of  that  duration  though 
one  of  the  individual  notes  may  be  located  there. 

It  is  possible  therefore  that  for  the  existence  of 
certain  sorts  of  objects,  e,g,  electrons,  minimum  quanta 
of  time  are  requisite.  Some  such  postulate  is  apparently 
indicated  by  the  modern  quantum  theory  and  it  is  per- 
fectly consistent  with  the  doctrine  of  objects  maintained 
in  these  lectures. 

Also  the  instance  of  the  distinction  between  the 
electron  as  the  mere  quantitative  electric  charge  of  its 
situation  and  the  electron  as  standing  for  the  ingression 
of  an  object  throughout  nature  illustrates  the  indefinite 
number  of  types  of  objects  which  exist  in  nature.  We 
can  intellectually  distinguish  even  subtler  and  subtler 
types  of  objects.  Here  I  reckon  subtlety  as  meaning 
seclusion  from  the  immediate  apprehension  of  sense- 
awareness.  Evolution  in  the  complexity  of  life  means  an 


VII]  OBJECTS  163 

increase  in  the  types  of  objects  directly  sensed.  Deli- 
cacy of  sense-apprehension  means  perceptions  of  objects 
as  distinct  entities  which  are  mere  subtle  ideas  to  cruder 
sensibilities.  The  phrasing  of  music  is  a  mere  abstract 
subtlety  to  the  unmusical;  it  is  a  direct  sense-appre- 
hension to  the  initiated.  For  example,  if  we  could 
imagine  some  lowly  type  of  organic  being  thinking  and 
aware  of  our  thoughts,  it  would  wonder  at  the  abstract 
subtleties  in  which  we  indulge  as  we  think  of  stones 
and  bricks  and  drops  of  water  and  plants.  It  only  knows 
of  vague  undifferentiated  feelings  in  nature.  It  would 
consider  us  as  given  over  to  the  play  of  excessively 
abstract  intellects.  But  then  if  it  could  think,  it  would 
anticipate;  and  if  it  anticipated,  it  would  soon  per- 
ceive for  itself. 

In  these  lectures  we  have  been  scrutinising  the 
foundations  of  natural  philosophy.  We  are  stopping  at 
the  very  point  where  a  boundless  ocean  of  enquiries 
opens  out  for  our  questioning. 

I  agree  that  the  view  of  Nature  which  I  have  main- 
tained in  these  lectures  is  not  a  simple  one.  Nature 
appears  as  a  complex  system  whose  factors  are  dimly 
discerned  by  us.  But,  as  I  ask  you.  Is  not  this  the  very 
truth  ?  Should  we  not  distrust  the  jaunty  assurance  with 
which  every  age  prides  itself  that  it  at  last  has  hit  upon 
the  ultimate  concepts  in  which  all  that  happens  can  be 
formulated }  The  aim  of  science  is  to  seek  the  simplest 
explanations  of  complex  facts.  We  are  apt  to  fall  into 
the  error  of  thinking  that  the  facts  are  simple  because 
simplicity  is  the  goal  of  our  quest.  The  guiding  motto 
in  the  life  of  every  natural  philosopher  should  be, 

Seek  simplicity  and  distrust  it. 

— — — ^ — "• —      -   -1^1 -^  »i  ^"^^"^ 


CHAPTER  VIII 
SUMMARY 

There  is  a  general  agreement  that  Einstein's  investiga- 
tions have  one  fundamental  merit  irrespective  of  any 
criticisms  which  we  may  feel  inclined  to  pass  on  them. 
They  have  made  us  think.  But  when  we  have  admitted 
so  far,  we  are  most  of  us  faced  with  a  distressing  per- 
plexity. What  is  it  that  we  ought  to  think  about?  The 
purport  of  my  lecture  this  afternoon  will  be  to  meet  this 
difficulty  and,  so  far  as  I  am  able,  to  set  in  a  clear  Ught 
the  changes  in  the  background  of  our  scientific  thought 
which  are  necessitated  by  any  acceptance,  however 
qualified,  of  Einstein's  main  positions.  I  remember  that 
I  am  lecturing  to  the  members  of  a  chemical  society 
who  are  not  for  the  most  part  versed  in  advanced 
mathematics.  The  first  point  that  I  would  urge  upon  you 
is  that  what  immediately  concerns  you  is  not  so  much 
the  detailed  deductions  of  the  new  theory  as  this  general 
change  in  the  background  of  scientific  conceptions 
which  will  follow  from  its  acceptance.  Of  course,  the 
detailed  deductions  are  important,  because  unless  our 
colleagues  the  astronomers  and  the  physicists  find  these 
predictions  to  be  verified  we  can  neglect  the  theory 
altogether.  But  we  may  now  take  it  as  granted  that  in 
many  striking  particulars  these  deductions  have  been 
found  to  be  in  agreement  with  observation.  Accord- 
ingly the  theory  has  to  be  taken  seriously  and  we  are 
anxious  to  know  what  will  be  the  consequences  of  its 
final  acceptance.  Furthermore  during  the  last  few  weeks 


CH.  VIII]  SUMMARY  165 

the  scientific  journals  and  the  lay  press  have  been  filled 
w^ith  articles  as  to  the  nature  of  the  crucial  experiments 
which  have  been  made  and  as  to  some  of  the  more 
striking  expressions  of  the  outcome  of  the  new  theory. 

*  Space  caught  bending'  appeared  on  the  news-sheet 
of  a  well-known  evening  paper.  This  rendering  is  a 
terse  but  not  inapt  translation  of  Einstein's  own  way  of 
interpreting  his  results.  I  should  say  at  once  that  I  am 
a  heretic  as  to  this  explanation  and  that  I  shall  expound 
to  you  another  explanation  based  upon  some  work  of 
my  own,  an  explanation  which  seems  to  me  to  be  more 
in  accordance  with  our  scientific  ideas  and  with  the 
whole  body  of  facts  which  have  to  be  explained.  We 
have  to  remember  that  a  new  theory  must  take  account 
of  the  old  well-attested  facts  of  science  just  as  much  as 
of  the  very  latest  experimental  results  which  have  led 
to  its  production. 

To  put  ourselves  in  the  position  to  assimilate  and  to 
criticise  any  change  in  ultimate  scientific  conceptions  we 
must  begin  at  the  beginning.  So  you  must  bear  with  me 
if  I  commence  by  making  some  simple  and  obvious 
reflections.  Let  us  consider  three  statements,  (i)  *  Yes- 
terday a  man  was  run  over  on  the  Chelsea  Embankment,' 
(ii)  *  Cleopatra's  Needle  is  on  the  Charing  Cross  Em- 
bankment,' and  (iii)  *  There  are  dark  lines  in  the  Solar 
Spectrum.'  The  first  statement  about  the  accident  to 
the  man  is  about  what  we  may  term  an  *  occurrence,' 
a  *  happening,'  or  an  *  event.'    I  will  use  the  term 

*  event '  because  it  is  the  shortest.  In  order  to  specify  an 
observed  event,  the  place,  the  time,  and  character  of  the 
event  are  necessary.  In  specifying  the  place  and  the  time 
you  are  really  stating  the  relation  of  the  assigned  event 
to  the  general  structure  of  other  observed  events.  For 


i66  THE  CONCEPT  OF  NATURE  [ch. 

example,  the  man  was  run  over  between  your  tea  and 
your  dinner  and  adjacently  to  a  passing  barge  in  the 
river  and  the  traffic  in  the  Strand.  The  point  which  I 
want  to  make  is  this:  Nature  is  known  to  us  in  our 
experience  as  a  complex  of  passing  events.  In  this 
complex  we  discern  definite  mutual  relations  between 
component  events,  which  we  may  call  their  relative 
positions,  and  these  positions  we  express  partly  in  terms 
of  space  and  partly  in  terms  of  time.  Also  in  addition 
to  its  mere  relative  position  to  other  events,  each  par- 
ticular event  has  its  own  peculiar  character.  In  other 
words,  nature  is  a  structure  of  events  and  each  event 
has  its  position  in  this  structure  and  its  own  peculiar 
character  or  quality. 

Let  us  now  examine  the  other  two  statements  in  the 
light  of  this  general  principle  as  to  the  meaning  of 
nature.  Take  the  second  statement,  *  Cleopatra's 
Needle  is  on  the  Charing  Cross  Embankment.'  At 
first  sight  we  should  hardly  call  this  an  event.  It  seems 
to  lack  the  element  of  time  or  transitoriness.  But  does 
it  ?  If  an  angel  had  made  the  remark  some  hundreds  of 
millions  of  years  ago,  the  earth  was  not  in  existence, 
twenty  millions  of  years  ago  there  was  no  Thames, 
eighty  years  ago  there  was  no  Thames  Embankment, 
and  when  I  was  a  small  boy  Cleopatra's  Needle  was 
not  there.  And  now  that  it  is  there,  we  none  of  us  expect 
it  to  be  eternal.  The  static  timeless  element  in  the  rela- 
tion of  Cleopatra's  Needle  to  the  Embankment  is  a 
pure  illusion  generated  by  the  fact  that  for  purposes  of 
daily  intercourse  its  emphasis  is  needless.  What  it 
comes  to  is  this :  Amidst  the  structure  of  events  which 
form  the  medium  within  which  the  daily  life  of  Lon- 
doners is  passed  we  know  how  to  identify  a  certain 


VIII]  SUMMARY  167 

stream  of  events  which  maintain  permanence  of  charac- 
ter, namely  the  character  of  being  the  situations  of 
Cleopatra's  Needle.  Day  by  day  and  hour  by  hour  we 
can  find  a  certain  chunk  in  the  transitory  life  of  nature 
and  of  that  chunk  we  say,  *  There  is  Cleopatra's  Needle/ 
If  we  define  the  Needle  in  a  sufficiently  abstract  manner 
we  can  say  that  it  never  changes.  But  a  physicist  who 
looks  on  that  part  of  the  life  of  nature  as  a  dance  of 
electrons,  will  tell  you  that  daily  it  has  lost  some  mole- 
cules and  gained  others,  and  even  the  plain  man  can 
see  that  it  gets  dirtier  and  is  occasionally  washed.  Thus 
the  question  of  change  in  the  Needle  is  a  mere  matter  of 
definition.  The  more  abstract  your  definition,  the  more 
permanent  the  Needle.  But  whether  your  Needle  change 
or  be  permanent,  all  you  mean  by  stating  that  it  is 
situated  on  the  Charing  Cross  Embankment,  is  that 
amid  the  structure  of  events  you  know  of  a  certain  con- 
tinuous limited  stream  of  events,  such  that  any  chunk 
of  that  stream,  during  any  hour,  or  any  day,  or  any 
second,  has  the  character  of  being  the  situation  of 
Cleopatra's  Needle. 

Finally,  we  come  to  the  third  statement,  *  There  are 
dark  lines  in  the  Solar  Spectrum.'  This  is  a  law  of  nature. 
But  what  does  that  mean  ?  It  means  merely  this.  If  any 
event  has  the  character  of  being  an  exhibition  of  the 
solar  spectrum  under  certain  assigned  circumstances,  it 
will  also  have  the  character  of  exhibiting  dark  lines  in 
that  spectrum. 

This  long  discussion  brings  us  to  the  final  conclusion 
that  the  concrete  facts  of  nature  are  events  exhibiting 
a  certain  structure  in  their  mutual  relations  and  certain 
characters  of  their  own.  The  aim  of  science  is  to  express 
the  relations  between  their  characters  in  terms  of  the 


i68  THE  CONCEPT  OF  NATURE  [ch. 

mutual  structural  relations  between  the  events  thus 
characterised.  The  mutual  structural  relations  between 
events  are  both  spatial  and  temporal.  If  you  think  of 
them  as  merely  spatial  you  are  omitting  the  temporal 
element,  and  if  you  think  of  them  as  merely  temporal 
you  are  omitting  the  spatial  element.  Thus  when  you 
think  of  space  alone,  or  of  time  alone,  you  are  dealing 
in  abstractions,  namely,  you  are  leaving  out  an  essential 
element  in  the  life  of  nature  as  known  to  you  in  the 
experience  of  your  senses.  Furthermore  there  are 
different  ways  of  making  these  abstractions  which  we 
think  of  as  space  and  as  time ;  and  under  some  circum- 
stances we  adopt  one  way  and  under  other  circumstances 
we  adopt  another  way.  Thus  there  is  no  paradox  in 
holding  that  what  we  mean  by  space  under  one  set  of 
circumstances  is  not  what  we  mean  by  space  under 
another  set  of  circumstances.  And  equally  what  we 
mean  by  time  under  one  set  of  circumstances  is  not 
what  we  mean  by  time  under  another  set  of  circum- 
stances. By  saying  that  space  and  time  are  abstractions, 
I  do  not  mean  that  they  do  not  express  for  us  real  facts 
about  nature.  What  I  mean  is  that  there  are  no  spatial 
facts  or  temporal  facts  apart  from  physical  nature, 
namely  that  space  and  time  are  merely  ways  of  expressing 
certain  truths  about  the  relations  between  events.  Also 
that  under  different  circumstances  there  are  different 
sets  of  truths  about  the  universe  which  are  naturally 
presented  to  us  as  statements  about  space.  In  such  a 
case  what  a  being  under  the  one  set  of  circumstances 
means  by  space  will  be  different  from  that  meant  by  a 
being  under  the  other  set  of  circumstances.  Accord- 
ingly when  we  are  comparing  two  observations  made 
under  different  circumstances  we  have  to  ask  '  Do  the 


VIII]  SUMMARY  169^ 

two  observers  mean  the  same  thing  by  space  and  the 
same  thing  by  time  ? '  The  modern  theory  of  relativity 
has  arisen  because  certain  perplexities  as  to  the  con- 
cordance of  certain  delicate  observations  such  as  the 
motion  of  the  earth  through  the  ether,  the  perihelion 
of  mercury,  and  the  positions  of  the  stars  in  the  neigh- 
bourhood of  the  sun,  have  been  solved  by  reference  to 
this  purely  relative  significance  of  space  and  time. 

I  want  now  to  recall  your  attention  to  Cleopatra^s 
Needle,  which  I  have  not  yet  done  with.  As  you  are 
walking  along  the  Embankment  you  suddenly  look  up 
and  say,  'Hullo,  there's  the  Needle.'  In  other  words, 
you  recognise  it.  You  cannot  recognise  an  event; 
because  when  it  is  gone,  it  is  gone.  You  may  observe 
another  event  of  analogous  character,  but  the  actual 
chunk  of  the  life  of  nature  is  inseparable  from  its  unique 
occurrence.  But  a  character  of  an  event  can  be  recog- 
nised. We  all  know  that  if  we  go  to  the  Embankment 
near  Charing  Cross  we  shall  observe  an  event  having  the 
character  which  we  recognise  as  Cleopatra's  Needle. 
Things  which  we  thus  recognise  I  call  objects.  An 
object  is  situated  in  those  events  or  in  that  stream  of 
events  of  which  it  expresses  the  character.  There  are 
many  sorts  of  objects.  For  example,  the  colour  green 
is  an  object  according  to  the  above  definition.  It  is  the 
purpose  of  science  to  trace  the  laws  which  govern  the 
appearance  of  objects  in  the  various  events  in  which  they 
are  found  to  be  situated.  For  this  purpose  we  can 
mainly  concentrate  on  two  types  of  objects,  which  I  will 
call  material  physical  objects  and  scientific  objects. 
A  material  physical  object  is  an  ordinary  bit  of  matter, 
Cleopatra's  Needle  for  example.  This  is  a  much  more 
complicated  type  of  object  than  a  mere  colour,  such  as 


I70  THE  CONCEPT  OF  NATURE  [ch. 

the  colour  of  the  Needle.  I  call  these  simple  objects, 
such  as  colours  or  sounds,  sense-objects.    An  artist 
will  train  himself  to  attend  more  particularly  to  sense- 
objects  where  the  ordinary  person  attends  normally  to 
material  objects.  Thus  if  you  were  walking  with  an 
artist,  when  you  said  *  There's  Cleopatra's  Needle,' 
perhaps  he  simultaneously  exclaimed  'There's  a  nice 
bit  of  colour.'    Yet  you  were  both  expressing  your 
recognition  of  different  component  characters  of  the 
same  event.    But  in  science  we  have  found  out  that 
when  we  know  all  about  the  adventures  amid  events  of 
material  physical  objects  and  of  scientific  objects  we 
have  most  of  the  relevant  information  which  will  enable 
us  to  predict  the  conditions  under  which  we  shall 
perceive  sense-objects  in  specific  situations.    For  ex- 
ample, when  we  know  that  there  is  a  blazing  fire  (i.e. 
material    and    scientific    objects    undergoing    various 
exciting  adventures  amid  events)  and  opposite  to  it  a 
mirror   (which   is   another   material   object)   and   the 
positions  of  a  man's  face  and  eyes  gazing  into  the  mirror, 
we  know  that  he  can  perceive  the  redness  of  the  flame 
situated  in  an  event  behind  the  mirror — thus,  to  a  large 
extent,  the  appearance  of  sense-objects  is  conditioned 
by  the  adventures  of  material  objects.  The  analysis  of 
these  adventures  makes  us  aware  of  another  character 
of  events,  namely  their  characters  as  fields  of  activity 
which  determine  the  subsequent  events  to  which  they 
will  pass  on  the  objects  situated  in  them.  We  express 
these  fields  of  activity  in  terms  of  gravitational,  electro- 
magnetic, or  chemical  forces  and  attractions.   But  the 
exact  expression  of  the  nature  of  these  fields  of  activity 
forces  us  intellectually  to  acknowledge  a  less  obvious 
type  of  objects  as  situated  in  events.  I  mean  molecules 


VIII]  SUMMARY  17: 

and  electrons.  These  objects  are  not  recognised  in 
isolation.  We  cannot  well  miss  Cleopatra's  Needle,  if 
we  are  in  its  neighbourhood ;  but  no  one  has  seen  a  single 
molecule  or  a  single  electron,  yet  the  characters  of 
events  are  only  explicable  to  us  by  expressing  them  in 
terms  of  these  scientific  objects .  Undoubtedly  molecules 
and  electrons  are  abstractions.  But  then  so  is  Cleo- 
patra's Needle.  The  concrete  facts  are  the  events  them- 
selves— I  have  already  explained  to  you  that  to  be  an 
abstraction  does  not  mean  that  an  entity  is  nothing.  It 
merely  means  that  its  existence  is  only  one  factor  of  a 
Inore  concrete  element  of  nature.  So  an  electron  is 
abstract  because  you  cannot  wipe  out  the  whole  structure 
of  events  and  yet  retain  the  electron  in  existence.  In 
the  same  way  the  grin  on  the  cat  is  abstract;  and  the 
molecule  is  really  in  the  event  in  the  same  sense  as  the 
grin  is  really  on  the  cat's  face.  Now  the  more  ultimate 
sciences  such  as  Chemistry  or  Physics  cannot  express 
their  ultimate  laws  in  terms  of  such  vague  objects  as 
the  sun,  the  earth,  Cleopatra's  Needle,  or  a  human 
body.  Such  objects  more  properly  belong  to  Astro- 
nomy, to  Geology,  to  Engineering,  to  Archaeology, 
or  to  Biology.  Chemistry  and  Physics  only  deal  with 
them  as  exhibiting  statistical  complexes  of  the  effects 
of  their  more  intimate  laws.  In  a  certain  sense,  they 
only  enter  into  Physics  and  Chemistry  as  technological 
applications.  The  reason  is  that  they  are  too  vague. 
Where  does  Cleopatra's  Needle  begin  and  where  does 
it  end.?  Is  the  soot  part  of  it?  Is  it  a  different 
object  when  it  sheds  a  molecule  or  when  its  surface 
enters  into  chemical  combination  with  the  acid  of  a 
London  fog?  The  definiteness  and  permanence  of  the 
Needle  is  nothing  to  the  possible  permanent  definiteness 


172  THE  CONCEPT  OF  NATURE  [ch. 

of  a  molecule  as  conceived  by  science,  and  the  per- 
manent definiteness  of  a  molecule  in  its  turn  yields  to 
that  of  an  electron.  Thus  science  in  its  most  ultimate 
formulation  of  law  seeks  objects  with  the  most  per- 
manent definite  simplicity  of  character  and  expresses 
its  final  laws  in  terms  of  them. 

Again  when  we  seek  definitely  to  express  the  relations 
of  events  which  arise  from  their  spatio-temporal 
structure,  we  approximate  to  simplicity  by  progressively 
diminishing  the  extent  (both  temporal  and  spatial)  of 
the  events  considered.  For  example,  the  event  which 
is  the  life  of  the  chunk  of  nature  which  is  the  Needle 
during  one  minute  has  to  the  life  of  nature  within  a 
passing  barge  during  the  same  minute  a  very  complex 
spatio-temporal  relation.  But  suppose  we  progressively 
diminish  the  time  considered  to  a  second,  to  a  hun- 
dredth of  a  second,  to  a  thousandth  of  a  second,  and 
so  on.  As  we  pass  along  such  a  series  we  approximate 
to  an  ideal  simplicity  of  structural  relations  of  the  pairs 
of  events  successively  considered,  which  ideal  we  call 
the  spatial  relations  of  the  Needle  to  the  barge  at  some 
instant.  Even  these  relations  are  too  complicated  for  us, 
and  we  consider  smaller  and  smaller  bits  of  the  Needle 
and  of  the  barge.  Thus  we  finally  reach  the  ideal  of  an 
event  so  restricted  in  its  extension  as  to  be  without  ex- 
tension in  space  or  extension  in  time.  Such  an  event  is 
a  mere  spatial  point-flash  of  instantaneous  duration. 
I  call  such  an  ideal  event  an  *  event-particle.'  You  must 
not  think  of  the  world  as  ultimately  built  up  of  event- 
particles.  That  is  to  put  the  cart  before  the  horse.  The 
world  we  know  is  a  continuous  stream  of  occurrence 
which  we  can  discriminate  into  finite  events  forming  by 
their  overlappings  and  containings  of  each  other  and 


VIII]  SUMMARY  173 

separations  a  spatio-temporal  structure.  We  can  express 
the  properties  of  this  structure  in  terms  of  the  ideal 
limits  to  routes  of  approximation,  which  I  have  termed 
event-particles.  Accordingly  event-particles  are  abstrac- 
tions in  their  relations  to  the  more  concrete  events.  But 
then  by  this  time  you  will  have  comprehended  that  you 
cannot  analyse  concrete  nature  without  abstracting. 
Also  I  repeat,  the  abstractions  of  science  are  entities 
which  are  truly  in  nature,  though  they  have  no  meaning 
in  isolation  from  nature. 

The  character  of  the  spatio-temporal  structure  of 
events  can  be  fully  expressed  in  terms  of  relations 
between  these  more  abstract  event-particles.  The  ad- 
vantage of  dealing  with  event-particles  is  that  though 
they  are  abstract  and  complex  in  respect  to  the  finite 
events  which  we  directly  observe,  they  are  simpler 
than  finite  events  in  respect  to  their  mutual  relations. 
Accordingly  they  express  for  us  the  demands  of  an  ideal 
accuracy,  and  of  an  ideal  simplicity  in  the  exposition  of 
relations.  These  event-particles  are  the  ultimate  elements 
of  the  four-dimensional  space-time  manifold  which  the 
theory  of  relativity  presupposes.  You  will  have  observed 
that  each  event-particle  is  as  much  an  instant  of  time  as 
it  is  a  point  of  space.  I  have  called  it  an  instantaneous 
point-flash.  Thus  in  the  structure  of  this  space-time 
manifold  space  is  not  finally  discriminated  from  time, 
and  the  possibility  remains  open  for  diverse  modes  of 
discrimination  according  to  the  diverse  circumstances 
of  observers.  It  is  this  possibility  which  makes  the 
fundamental  distinction  between  the  new  way  of  con- 
ceiving the  universe  and  the  old  way.  The  secret  of 
understanding  relativity  is  to  understand  this.  It  is  of 
no  use  rushing  in  with  picturesque  paradoxes,  such  as 


174  THE  CONCEPT  OF  NATURE  [ch. 

*  Space  caught  bending,'  if  you  have  not  mastered  this 
fundamental  conception  which  underHes  the  whole 
theory.  When  I  say  that  it  underHes  the  whole  theory, 
I  mean  that  in  my  opinion  it  ought  to  underlie  it,  though 
I  may  confess  some  doubts  as  to  how  far  all  expositions 
of  the  theory  have  really  understood  its  implications  and 
its  premises. 

Our  measurements  when  they  are  expressed  in  terms 
of  an  ideal  accuracy  are  measurements  which  express 
properties  of  the  space-time  manifold.  Now  there  are 
measurements  of  different  sorts.  You  can  measure 
lengths,  or  angles,  or  areas,  or  volumes,  or  times.  There 
are  also  other  sorts  of  measures  such  as  measurements 
of  intensity  of  illumination,  but  I  will  disregard  these 
for  the  moment  and  will  confine  attention  to  those 
measurements  which  particularly  interest  us  as  being 
measurements  of  space  or  of  time.  It  is  easy  to  see  that 
four  such  measurements  of  the  proper  characters  are 
necessary  to  determine  the  position  of  an  event-particle 
in  the  space-time  manifold  in  its  relation  to  the  rest  of 
the  manifold.  For  example,  in  a  rectangular  field  you 
start  from  one  corner  at  a  given  time,  you  measure  a 
definite  distance  along  one  side,  you  then  strike  out 
into  the  field  at  right  angles,  and  then  measure  a  definite 
distance  parallel  to  the  other  pair  of  sides,  you  then  rise 
vertically  a  definite  height  and  take  the  time.  At  the 
point  and  at  the  time  which  you  thus  reach  there  is 
occurring  a  definite  instantaneous  point-flash  of  nature. 
In  other  words,  your  four  measurements  have  deter- 
mined a  definite  event-particle  belonging  to  the  four- 
dimension  space-time  manifold.  These  measurements 
have  appeared  to  be  very  simple  to  the  land-surveyor 
and  raise  in  his  mind  no  philosophic  difficulties.   But 


VIII]  SUMMARY  175 

suppose  there  are  beings  on  Mars  sufficiently  advanced 
in  scientific  invention  to  be  able  to  watch  in  detail  the 
operations  of  this  survey  on  earth.  Suppose  that  they 
construe  the  operations  of  the  English  land-surveyors 
in  reference  to  the  space  natural  to  a  being  on  Mars, 
namely  a  Martio-centric  space  in  which  that  planet  is 
fixed.  The  earth  is  moving  relatively  to  Mars  and  is 
rotating.  To  the  beings  on  Mars  the  operations,  con- 
strued in  this  fashion,  effect  measurements  of  the  greatest 
complication.  Furthermore,  according  to  the  relati- 
vistic  doctrine,  the  operation  of  time-measurement  on 
earth  will  not  correspond  quite  exactly  to  any  time- 
measurement  on  Mars. 

I  have  discussed  this  example  in  order  to  make  you 
realise  that  in  thinking  of  the  possibilities  of  measure- 
ment in  the  space-time  manifold,  we  must  not  confine 
ourselves  merely  to  those  minor  variations  which  might 
seem  natural  to  human  beings  on  the  earth.  Let  us 
make  therefore  the  general  statement  that  four  measure- 
ments, respectively  of  independent  types  (such  as  mea- 
surements of  lengths  in  three  directions  and  a  time), 
can  be  found  such  that  a  definite  event-particle  is 
determined  by  them  in  its  relations  to  other  parts  of 
the  manifold. 

I^  (Ply  p2^  p3y  P^)  ^^  ^  set  of  measurements  of  this 
system,  then  the  event-particle  which  is  thus  deter- 
mined will  be  said  to  have  />i,  p^,  p^y  ^4  as  its  co-ordi- 
nates in  this  system  of  measurement.  Suppose  that  we 
name  it  the/)-system  of  measurement.  Then  in  the  same 
/>-system  by  properly  varying  (/>!,  p^,  p^y  p^  every 
event-particle  that  has  been,  or  will  be,  or  instantane- 
ously is  now,  can  be  indicated.  Furthermore,  according 
to  any  system  of  measurement  that  is  natural  to  us. 


176  THE  CONCEPT  OF  NATURE  [ch. 

three  of  the  co-ordinates  will  be  measurements  of  space 
and  one  will  be  a  measurement  of  time.  Let  us  always 
take  the  last  co-ordinate  to  represent  the  time-measure- 
ment. Then  we  should  naturally  say  that  (/>i,  />2,  Pz) 
determined  a  point  in  space  and  that  the  event-particle 
happened  at  that  point  at  the  tivatp^.  But  we  must  not 
make  the  mistake  of  thinking  that  there  is  a  space  in 
addition  to  the  space-time  manifold.  That  manifold  is 
all  that  there  is  for  the  determination  of  the  meaning  of 
space  and  time.  We  have  got  to  determine  the  meaning 
of  a  space-point  in  terms  of  the  event-particles  of  the 
four-dimensional  manifold.  There  is  only  one  way  to 
do  this.  Note  that  if  we  vary  the  time  and  take  times 
with  the  same  three  space  co-ordinates,  then  the  event- 
particles,  thus  indicated,  are  all  at  the  same  point.  But 
seeing  that  there  is  nothing  else  except  the  event- 
particles,  this  can  only  mean  that  the  point  (pi,  />2>  p^ 
of  the  space  in  the  /)-system  is  merely  the  collection  of 
event-particles  (/>!,  p^,  p^,  [pj))  where /)4  is  varied  and 
(pi,  p2y  Pz)  is  kept  fixed.  It  is  rather  disconcerting  to 
find  that  a  point  in  space  is  not  a  simple  entity ;  but  it 
is  a  conclusion  which  follows  immediately  from  the 
relative  theory  of  space. 

Furthermore  the  inhabitant  of  Mars  determines 
event-particles  by  another  system  of  measurements. 
Call  his  system  the  ^-system.  According  to  him 
{qiy  q2,  ^3,  g'4)  determines  an  event-particle,  and 
(^1,  ^2>  ^3)  determines  a  point  and  ^4  a  time.  But  the 
collection  of  event-particles  which  he  thinks  of  as  a 
point  is  entirely  different  from  any  such  collection 
which  the  man  on  earth  thinks  of  as  a  point.  Thus  the 
^-space  for  the  man  on  Mars  is  quite  different  from  the 
^-space  for  the  land-surveyor  on  earth. 


VIII]  SUMMARY  177 

So  far  in  speaking  of  space  we  have  been  talking  of 
the  timeless  space  of  physical  science,  namely,  of  our 
concept  of  eternal  space  in  v^hich  the  world  adventures. 
But  the  space  which  we  see  as  we  look  about  is  instan- 
taneous space.  Thus  if  our  natural  perceptions  are 
adjustable  to  the  ^-system  of  measurements  we  see 
instantaneously  all  the  event-particles  at  some  definite 
time  ^4,  and  observe  a  succession  of  such  spaces  as  time 
moves  on.  The  timeless  space  is  achieved  by  stringing 
together  all  these  instantaneous  spaces.  The  points  of 
an  instantaneous  space  are  event-particles,  and  the 
points  of  an  eternal  space  are  strings  of  event-particles 
occurring  in  succession.  But  the  man  on  Mars  will 
never  perceive  the  same  instantaneous  spaces  as  the 
man  on  the  earth.  This  system  of  instantaneous  spaces 
will  cut  across  the  earth-man's  system.  For  the  earth- 
man  there  is  one  instantaneous  space  which  is  the 
instantaneous  present,  there  are  the  past  spaces  and  the 
future  spaces.  But  the  present  space  of  the  man  on 
Mars  cuts  across  the  present  space  of  the  man  on  the 
earth.  So  that  of  the  event-particles  which  the  earth- 
man  thinks  of  as  happening  now  in  the  present,  the 
man  on  Mars  thinks  that  some  are  already  past  and  are 
ancient  history,  that  others  are  in  the  future,  and  others 
are  in  the  immediate  present.  This  break-down  in  the 
neat  conception  of  a  past,  a  present,  and  a  future  is  a 
serious  paradox.  I  call  two  event-particles  which  on 
some  or  other  system  of  measurement  are  in  the  same 
instantaneous  space  *  co-present'  event-particles.  Then 
it  is  possible  that  A  and  B  may  be  co-present,  and  that 
A  and  C  may  be  co-present,  but  that  B  and  C  may  not 
be  co-present.  For  example,  at  some  inconceivable 
distance  from  us  there  are  events  co-present  with  us 

W.N.  12 


178  THE  CONCEPT  OF  NATURE  [ch. 

now  and  also  co-present  with  the  birth  of  Queen 
Victoria.  If  A  and  B  are  co-present  there  will  be  some 
systems  in  which  A  precedes  B  and  some  in  which  B 
precedes  A,  Also  there  can  be  no  velocity  quick  enough 
to  carry  a  material  particle  from  ^  to  j5  or  from  B  to  A. 
These  different  measure-systems  with  their  divergences 
of  time-reckoning  are  puzzling,  and  to  some  extent 
affront  our  common  sense.  It  is  not  the  usual  way  in 
which  we  think  of  the  Universe.  We  think  of  one 
necessary  time-system  and  one  necessary  space.  Ac- 
cording to  the  new  theory,  there  are  an  indefinite 
number  of  discordant  time-series  and  an  indefinite 
number  of  distinct  spaces.  Any  correlated  pair,  a 
time-system  and  a  space-system,  will  do  in  which  to  fit 
our  description  of  the  Universe.  We  find  that  under 
given  conditions  our  measurements  are  necessarily  made 
in  some  one  pair  which  together  form  our  natural 
measure-system.  The  difficulty  as  to  discordant  time- 
systems  is  partly  solved  by  distinguishing  between  what 
I  call  the  creative  advance  of  nature,  which  is  not 
properly  serial  at  all,  and  any  one  time  series.  We 
habitually  muddle  together  this  creative  advance,  which 
we  experience  and  know  as  the  perpetual  transition  of 
nature  into  novelty,  with  the  single- time  series  which 
we  naturally  employ  for  measurement.  The  various 
time-series  each  measure  some  aspect  of  the  creative 
advance,  and  the  whole  bundle  of  them  express  all  the 
properties  of  this  advance  which  are  measurable.  The 
reason  why  we  have  not  previously  noted  this  difference 
of  time-series  is  the  very  small  difference  of  properties 
between  any  two  such  series.  Any  observable  pheno- 
mena due  to  this  cause  depend  on  the  square  of  the 
ratio  of  any  velocity  entering  into  the  observation  to 


VIII]  SUMMARY  179 

the  velocity  of  light.  Now^  Ught  takes  about  fifty  minutes 
to  get  round  the  earth's  orbit;  and  the  earth  takes 
rather  more  than  17,531  half-hours  to  do  the  same. 
Hence  all  the  effects  due  to  this  motion  are  of  the  order 
of  the  ratio  of  one  to  the  square  of  10,000.  Accordingly 
an  earth-man  and  a  sun-man  have  only  neglected 
effects  whose  quantitative  magnitudes  all  contain  the 
factor  i/io^.  Evidently  such  effects  can  only  be  noted 
by  means  of  the  most  refined  observations.  They  have 
been  observed  how^ever.  Suppose  wc  compare  two 
observations  on  the  velocity  of  light  made  with  the 
same  apparatus  as  we  turn  it  through  a  right  angle. 
The  velocity  of  the  earth  relatively  to  the  sun  is  in  one 
direction,  the  velocity  of  light  relatively  to  the  ether 
should  be  the  same  in  all  directions.  Hence  if  space 
when  we  take  the  ether  as  at  rest  means  the  same  thing 
as  space  when  we  take  the  earth  as  at  rest,  we  ought  to 
find  that  the  velocity  of  light  relatively  to  the  earth 
varies  according  to  the  direction  from  which  it  comes. 

These  observations  on  earth  constitute  the  basic 
principle  of  the  famous  experiments  designed  to  detect 
the  motion  of  the  earth  through  the  ether.  You  all 
know  that,  quite  unexpectedly,  they  gave  a  null  result. 
This  is  completely  explained  by  the  fact  that,  the  space- 
system  and  the  time-system  which  we  are  using  are 
in  certain  minute  ways  different  from  the  space  and  the 
time  relatively  to  the  sun  or  relatively  to  any  other  body 
with  respect  to  which  it  is  moving. 

All  this  discussion  as  to  the  nature  of  time  and  space 
has  lifted  above  our  horizon  a  great  difficulty  which 
affects  the  formulation  of  all  the  ultimate  laws  of  physics 
— for  example,  the  laws  of  the  electromagnetic  field, 
and  the  law  of  gravitation.    Let  us  take  the  law  of 


i8o  THE  CONCEPT  OF  NATURE  [CH. 

gravitation  as  an  example.  Its  formulation  is  as  follows : 
Two  material  bodies  attract  each  other  with  a  force 
proportional  to  the  product  of  their  masses  and  umka 
versely  proportional  to  the  square  of  their  distances.  In 
this  statement  the  bodies  are  supposed  to  be  small 
enough  to  be  treated  as  material  particles  in  relation  to 
their  distances;  and  we  need  not  bother  further  about 
that  minor  point.  The  difficulty  to  which  I  want  to 
draw  your  attention  is  this :  In  the  formulation  of  the 
law  one 'definite  time  and  one  definite  space  are  pre- 
supposed. The  two  masses  are  assumed  to  be  in  simul- 
taneous positions. 

But  what  is  simultaneous  in  one  time-system  may  not 
be  simultaneous  in  another  time-system.  So  according 
to  our  new  views  the  law  is  in  this  respect  not  formulated 
so  as  to  have  any  exact  meaning.  Furthermore  an 
analogous  difficulty  arises  over  the  question  of  distance. 
The  distance  between  two  instantaneous  positions, 
i.e,  between  two  event-particles,  is  different  in  different 
space-systems.  What  space  is  to  be  chosen  ?  Thus  again 
the  law  lacks  precise  formulation,  if  relativity  is  accepted. 
Our  problem  is  to  seek  a  fresh  interpretation  of  the 
law  of  gravity  in  which  these  difficulties  are  evaded.  In 
the  first  place  we  must  avoid  the  abstractions  of  space 
and  time  in  the  formulation  of  our  fundamental  ideas 
and  must  recur  to  the  ultimate  facts  of  nature,  namely 
to  events.  Also  in  order  to  find  the  ideal  simplicity  of 
expressions  of  the  relations  between  events,  we  restrict 
ourselves  to  event-particles.  Thus  the  life  of  a  material 
particle  is  its  adventure  amid  a  track  of  event-particles 
strung  out  as  a  continuous  series  or  path  in  the  four- 
dimensional  space-time  manifold.  These  event-particles 
are  the  various  situations  of  the  material  particle.  We 


viiij  SUMMARY  i8i 

usually  express  this  fact  by  adopting  our  natural  space- 
time  system  and  by  talking  of  the  path  in  space  of  the 
material  particle  as  it  exists  at  successive  instants  of  time. 

We  have  to  ask  ourselves  what  are  the  laws  of  nature 
which  lead  the  material  particle  to  adopt  just  this  path 
among  event-particles  and  no  other.  Think  of  the  path 
as  a  whole.  What  characteristic  has  that  path  got  which 
would  not  be  shared  by  any  other  slightly  varied  path  ? 
We  are  asking  for  more  than  a  law  of  gravity.  We  want 
laws  of  motion  and  a  general  idea  of  the  way  to  formulate 
the  effects  of  physical  forces. 

In  order  to  answer  our  question  we  put  the  idea  of  the 
attracting  masses  in  the  background  and  concentrate 
attention  on  the  field  of  activity  of  the  events  in  the 
neighbourhood  of  the  path.  In  so  doing  we  are  acting 
in  conformity  with  the  whole  trend  of  scientific  thought 
during  the  last  hundred  years,  which  has  more  and  more 
concentrated  attention  on  the  field  of  force  as  the  im- 
mediate agent  in  directing  motion,  to  the  exclusion  of 
the  consideration  of  the  immediate  mutual  influence 
between  two  distant  bodies.  We  have  got  to  find  the 
way  of  expressing  the  field  of  activity  of  events  in  the 
neighbourhood  of  some  definite  event-particle  E  of  the 
four-dimensional  manifold.  I  bring  in  a  fundamental 
physical  idea  which  I  call  the  *  impetus '  to  express  this 
physical  field.  The  event-particle  E  is  related  to  any 
neighbouring  event-particle  P  by  an  element  of  impetus. 
The  assemblage  of  all  the  elements  of  impetus  relating 
E  to  the  assemblage  of  event-particles  in  the  neighbour- 
hood of  E  expresses  the  character  of  the  field  of  activity 
in  the  neighbourhood  of  E,  Where  I  differ  from  Einstein 
is  that  he  conceives  this  quantity  which  I  call  the  impetus 
as  merely  expressing  the  characters  of  the  space  and 


i82  THE  CONCEPT  OF  NATURE  [ch. 

time  to  be  adopted  and  thus  ends  by  talking  of  the 
gravitational  field  expressing  a  curvature  in  the  space- 
time  manifold.  I  cannot  attach  any  clear  conception  to 
his  interpretation  of  space  and  time.  My  formulae 
differ  slightly  from  his,  though  they  agree  in  those 
instances  where  his  results  have  been  verified.  I  need 
hardly  say  that  in  this  particular  of  the  formulation  of  the 
law  of  gravitation  I  have  drawn  on  the  general  method 
of  procedure  which  constitutes  his  great  discovery. 

Einstein  showed  how  to  express  the  characters  of  the 
assemblage  of  elements  of  impetus  of  the  field  sur- 
rounding an  event-particle  E  in  terms  of  ten  quantities 

which  I  will  call  J^*  J12  (=  .72i).  J22.  J23  (=  ^32).  etc. 
It  will  be  noted  that  there  are  four  spatio-temporal 
measurements  relating  E  to  its  neighbour  P,  and  that 
there  are  ten  pairs  of  such  measurements  if  we  are 
allowed  to  take  any  one  measurement  twice  over  to 
make  one  such  pair.  The  ten  J's  depend  merely  on  the 
position  of  E  in  the  four-dimensional  manifold,  and  the 
element  of  impetus  between  E  and  P  can  be  expressed 
in  terms  of  the  ten  J's  and  the  ten  pairs  of  the  four 
spatio-temporal  measurements  relating  E  and  P.  The 
numerical  values  of  the  J's  will  depend  on  the  system 
of  measurement  adopted,  but  are  so  adjusted  to  each 
particular  system  that  the  same  value  is  obtained  for 
the  element  of  impetus  between  E  and  P,  whatever  be 
the  system  of  measurement  adopted.  This  fact  is  ex- 
pressed by  saying  that  the  ten  J's  form  a  '  tensor.'  It  is 
not  going  too  far  to  say  that  the  announcement  that 
physicists  would  have  in  future  to  study  the  theor^^ 
of  tensors  created  a  veritable  panic  among  them  when 
the  verification  of  Einstein's  predictions  was  first 
announced. 


VIII]  SUMMARY  183 

The  ten  J's  at  any  event-particle  E  can  be  expressed  in 
terms  of  tw^o  functions  w^hich  I  call  the  potential  and  the 
*  associate-potential'  at  E.  The  potential  is  practically 
what  is  meant  by  the  ordinary  gravitation  potential, 
when  we  express  ourselves  in  terms  of  the  Euclidean 
space  in  reference  to  which  the  attracting  mass  is  at 
rest.  The  associate-potential  is  defined  by  the  modifi- 
cation of  substituting  the  direct  distance  for  the  inverse 
distance  in  the  definition  of  the  potential,  and  its  calcu- 
lation can  easily  be  made  to  depend  on  that  of  the  old- 
fashioned  potential.  Thus  the  calculation  of  the  J's — the 
coefficients  of  impetus,  as  I  will  call  them — does  not 
involve  anything  very  revolutionary  in  the  mathematical 
knowledge  of  physicists.  We  now  return  to  the  path  of 
the  attracted  particle.  We  add  up  all  the  elements  of 
impetus  in  the  whole  path,  and  obtain  thereby  what  I 
call  the  'integral  impetus.'  The  characteristic  of  the 
actual  path  as  compared  with  neighbouring  alternative 
paths  is  that  in  the  actual  paths  the  integral  impetus 
would  neither  gain  nor  lose,  if  the  particle  wobbled  out 
of  it  into  a  small  extremely  near  alternative  path.  Mathe- 
maticians would  express  this  by  saying,  that  the  integral 
impetus  is  stationary  for  an  infinitesimal  displacement. 
In  this  statement  of  the  law  of  motion  I  have  neglected 
the  existence  of  other  forces.  But  that  would  lead  me 
too  far  afield. 

The  electromagnetic  theory  has  to  be  modified  to 
allow  for  the  presence  of  a  gravitational  field.  Thus 
Einstein's  investigations  lead  to  the  first  discovery  of 
any  relation  between  gravity  and  other  physical  pheno- 
mena. In  the  form  in  which  I  have  put  this  modification, 
we  deduce  Einstein's  fundamental  principle,  as  to  the 
motion  of  light  along  its  rays,  as  a  first  approximation 


i84  THE  CONCEPT  OF  NATURE         [ch.  viii 

which  IS  absolutely  true  for  infinitely  short  waves. 
Einstein's  principle,  thus  partially  verified,  stated  in  my 
language  is  that  a  ray  of  light  always  follows  a  path  such 
that  the  integral  impetus  along  it  is  zero.  This  involves 
that  every  element  of  impetus  along  it  is  zero. 

In  conclusion,  I  must  apologise.  In  the  first  place 
I  have  considerably  toned  down  the  various  exciting 
peculiarities  of  the  original  theory  and  have  reduced  it 
to  a  greater  conformity  with  the  older  physics.  I  do  not 
allow  that  physical  phenomena  are  due  to  oddities  of 
space.  Also  I  have  added  to  the  dullness  of  the  lecture 
by  my  respect  for  the  audience.  You  would  have  enjoyed 
a  more  popular  lecture  with  illustrations  of  delightful 
paradoxes.  But  I  know  also  that  you  are  serious 
students  who  are  here  because  you  really  want  to  know 
how  the  new  theories  may  aflFect  your  scientific  re- 
searches. 


CHAPTER  IX 
THE  ULTIMATE  PHYSICAL  CONCEPTS 

The  second  chapter  of  this  book  lays  down  the  first 
principle  to  be  guarded  in  framing  our  physical  concept. 
We  must  avoid  vicious  bifurcation  Nature  is  nothing 
else  than  the  deliverance  of  sense-awareness.  We  have 
no  principles  whatever  to  tell  us  what  could  stimulate 
mind  towards  sense-awareness.  Our  sole  task  is  to 
exhibit  in  one  system  the  characters  and  inter-relations 
of  all  that  is  observed.  Our  attitude  towards  nature  is 
purely  *  behaviouristic,'  so  far  as  concerns  the  formulation 
of  physical  concepts. 

Our  knowledge  of  nature  is  an  experience  of  activity 
(or  passage).  The  things  previously  observed  are  active 
entities,  the  *  events.'  They  are  chunks  in  the  life  of 
nature.  These  events  have  to  each  other  relations  which 
in  our  knowledge  differentiate  themselves  into  space- 
relations  and  time-relations.  But  this  differentiation 
between  space  and  time,  though  inherent  in  nature,  is 
comparatively  superficial ;  and  space  and  time  are  each 
partial  expressions  of  one  fundamental  relation  between 
events  which  is  neither  spatial  nor  temporal.  This 
relation  I  call  'extension.'  The  relation  of  'extending 
over'  is  the  relation  of  'including,'  either  in  a  spatial  or 
in  a  temporal  sense,  or  in  both.  But  the  mere  'inclu- 
sion' is  more  fundamental  than  either  alternative  and 
does  not  require  any  spatio-temporal  differentiation. 
In  respect  to  extension  two  events  are  mutually  related 
so  that  either  (i)  one  includes  the  other,  or  (ii)  one  over- 
laps the  other  without  complete  inclusion,  or  (iii)  they 


i86  THE  CONCEPT  OF  NATURE  [CH. 

are  entirely  separate.  But  great  care  is  required  in  the 
definition  of  spatial  and  temporal  elements  from  this 
basis  in  order  to  avoid  tacit  limitations  really  depend- 
ing on  undefined  relations  and  properties. 

Such  fallacies  can  be  avoided  by  taking  account  of 
two  elements  in  our  experience,  namely,  (i)  our  ob- 
servational *  present,'  and  (ii)  our  *  percipient  event.' 

Our  observational  *  present '  is  what  I  call  a  *  duration.' 
It  is  the  whole  of  nature  apprehended  in  our  immediate 
observation.  It  has  therefore  the  nature  of  an  event, 
but  possesses  a  peculiar  completeness  which  marks  out 
such  durations  as  a  special  type  of  events  inherent  in 
nature.  A  duration  is  not  instantaneous.  It  is  all  that 
there  is  of  nature  with  certain  temporal  limitations.  In 
contradistinction  to  other  events  a  duration  will  be 
called  infinite  and  the  other  events  are  finite^.  In  our 
knowledge  of  a  duration  we  distinguish  (i)  certain 
included  events  which  are  particularly  discriminated 
as  to  their  peculiar  individualities,  and  (ii)  the  remaining 
included  events  which  are  only  known  as  necessarily  in 
being  by  reason  of  their  relations  to  the  discriminated 
events  and  to  the  whole  duration.  The  duration  as  a 
whole  is  signified^  by  that  quality  of  relatedness  (in 
respect  to  extension)  possessed  by  the  part  which  is 
^immediately  under  observation;  namely,  by  the  fact 
;  that  there  is  essentially  a  beyond  to  whatever  is  observed. 
\  I  mean  by  this  that  every  event  is  known  as  being  related 
\to  other  events  which  it  does  not  include.  This  fact, 
jthat  every  event  is  known  as  possessing  the  quality  of 
^exclusion,  shows  that  exclusion  is  as  positive  a  relation 
as  inclusion.  There  are  of  course  no  merely  negative 


^  Cf.  note  on  ^significance,'  pp.  197,  198. 
2  Cf.  Ch.  Ill,  pp.  51  et  seq. 


IX]      THE  ULTIMATE  PHYSICAL  CONCEPTS     187 

relations  in  nature,  and  exclusion  is  not  the  mere 
negative  of  inclusion,  though  the  two  relations  are 
contraries.    Both  relations  are  concerned  solely  with^ 
events,  and  exclusion  is  capable  of  logical  definition  in 
terms  of  inclusion. 

Perhaps  the  most  obvious  exhibition  of  significance 
is  to  be  found  in  our  knowledge  of  the  geometrical 
character  of  events  inside  an  opaque  material  object. 
For  example  we  know  that  an  opaque  sphere  has  a 
centre.  This  knowledge  has  nothing  to  do  with  the 
material;  the  sphere  may  be  a  solid  uniform  billiard 
ball  or  a  hollow  lawn-tennis  ball.  Such  knowledge  is 
essentially  the  product  of  significance,  since  the  general 
character  of  the  external  discriminated  events  has  in- 
formed us  that  there  are  events  within  the  sphere  and 
has  also  informed  us  of  their  geometrical  structure. 

Some  criticisms  on  *The  Principles  of  Natural 
Knowledge'  show  that  difficulty  has  been  found  in 
apprehending  durations  as  real  stratifications  of  nature. 
I  think  that  this  hesitation  arises  from  the  unconscious 
influence  of  the  vicious  principle  of  bifurcation,  so 
deeply  embedded  in  modern  philosophical  thought. 
We  observe  nature  as  extended  in  an  immediate  present 
which  is  simultaneous  but  not  instantaneous,  and  there- 
fore the  whole  which  is  immediately  discerned  or 
signified  as  an  inter-related  system  forms  a  stratification 
of  nature  which  is  a  physical  fact.  This  conclusion 
immediately  follows  unless  we  admit  bifurcation  in  the 
form  of  the  principle  of  psychic  additions,  here  rejected. 

Our  *  percipient  event '  is  that  event  included  in  our 
observational  present  which  we  distinguish  as  being  in 
some  peculiar  way  our  standpoint  for  perception.  It  is 
roughly  speaking  that  event  which  is  our  bodily  life 


i88  THE  CONCEPT  OF  NATURE  [CH. 

within  the  present  duration.  The  theory  of  perception 
as  evolved  by  medical  psychology  is  based  on  signifi- 
cance. The  distant  situation  of  a  perceived  object  is 
merely  known  to  us  as  signified  by  our  bodily  state, 
i,e,  by  our  percipient  event.  In  fact  perception  requires 
sense-awareness  of  the  significations  of  our  percipient 
event  together  with  sense-awareness  of  a  peculiar  re- 
lation (situation)  between  certain  objects  and  the  events 
thus  signified.   Our  percipient  event  is  saved  by  being 
the  whole  of  nature  by  this  fact  of  its  significations. 
This  is  the  meaning  of  calling  the  percipient  event 
our  standpoint  for  perception.  The  course  of  a  ray  of 
light  is  only  derivatively  connected  with  perception. 
What  we  do  perceive  are  objects  as  related  to  events 
signified   by   the   bodily   states   excited    by    the    ray. 
These  signified  events  (as  is  the  case  of  images  seen 
behind  a  mirror)  may  have  very  little  to  do  with  the 
actual  course  of  the  ray.  In  the  course  of  evolution  those 
animals  have  survived  whose  sense-awareness  is  con- 
centrated on  those  significations  of  their  bodily  states 
which  are  on  the  average  important  for  their  welfare. 
The  whole  world  of  events  is  signified,  but  there  are 
some  which  exact  the  death  penalty  for  inattention. 

The  percipient  event  is  always  here  and  now  in  the 
associated  present  duration.  It  has,  what  may  be  called, 
an  absolute  position  in  that  duration.  Thus  one  definite 
duration  is  associated  with  a  definite  percipient  event, 
and  we  are  thus  aware  of  a  peculiar  relation  which 
finite  events  can  bear  to  durations.  I  call  this  relation 
*  cogredience.'  The  notion  of  rest  is  derivative  from  that 
of  cogredience,  and  the  notion  of  motion  is  derivative 
from  that  of  inclusion  within  a  duration  without  cogre- 
dience with  it.  In  fact  motion  is  a  relation  (of  varying 


IX]      THE  ULTIMATE  PHYSICAL  CONCEPTS     189 

character)  between  an  observed  event  and  an  observed 
duration,  and  cogredience  is  the  most  simple  character 
or  subspecies  of  motion.  To  sum  up,  a  duration  and  a 
percipient  event  are  essentially  involved  in  the  general 
character  of  each  observation  of  nature,  and  the  per- 
cipient event  is  cogredient  with  the  duration. 

Our  knowledge  of  the  peculiar  characters  of  different 
events  depends  upon  our  power  of  comparison.  I  call 
the  exercise  of  this  factor  in  our  knowledge*  recognition,' 
and  the  requisite  sense-awareness  of  the  comparable 
characters  I  call  *  sense-recognition.'  Recognition  and 
abstraction  essentially  involve  each  other.  Each  of  them 
exhibits  an  entity  for  knowledge  which  is  less  than  the 
concrete  fact,  but  is  a  real  factor  in  that  fact.  The  most 
concrete  fact  capable  of  separate  discrimination  is  the 
event.  We  cannot  abstract  without  recognition,  and 
we  cannot  recognise  without  abstraction.  Perception 
involves  apprehension  of  the  event  and  recognition  of 
the  factors  of  its  character. 

The  things  recognised  are  what  I  call  *  objects.'  In 
this  general  sense  of  the  term  the  relation  of  extension 
is  itself  an  object.  In  practice  however  I  restrict  the 
term  to  those  objects  which  can  in  some  sense  or  other 
be  said  to  have  a  situation  in  an  event;  namely,  in  the 
phrase  '  There  it  is  again '  I  restrict  the  *  there '  to  be  the 
indication  of  a  special  event  which  is  the  situation  of  the 
object.  Even  so,  there  are  different  types  of  objects,  and 
statements  which  are  true  of  objects  of  one  type  are  not 
in  general  true  of  objects  of  other  types.  The  objects 
with  which  we  are  here  concerned  in  the  formulation 
of  physical  laws  are  material  objects,  such  as  bits  of 
matter,  molecules  and  electrons.  An  object  of  one  of 
these  types  has  relations  to  events  other  than  those 


190  THE  CONCEPT  OF  NATURE  [ch. 

belonging  to  the  stream  of  its  situations.  The  fact  of  its 
situations  within  this  stream  has  impressed  on  all  other 
events  certain  modifications  of  their  characters.  In 
truth  the  object  in  its  completeness  may  be  conceived 
as  a  specific  set  of  correlated  modifications  of  the  charac- 
ters of  all  events,  with  the  property  that  these  modifica- 
tions attain  to  a  certain  focal  property  for  those  events 
which  belong  to  the  stream  of  its  situations.  The  total 
assemblage  of  the  modifications  of  the  characters  of 
events  due  to  the  existence  of  an  object  in  a  stream  of 
situations  is  what  I  call  the  'physical  field'  due  to  the 
object. .  But  the  object  cannot  really  be  separated  from 
its  field.  The  object  is  in  fact  nothing  else  than  the 
systematically  adjusted  set  of  modifications  of  the  field. 
The  conventional  limitation  of  the  object  to  the  focal 
stream  of  events  in  which  it  is  said  to  be  '  situated '  is 
convenient  for  some  purposes,  but  it  obscures  the 
ultimate  fact  of  nature.  From  this  point  of  view  the 
antithesis  between  action  at  a  distance  and  action  by 
transmission  is  meaningless.  The  doctrine  of  this  para- 
graph is  nothing  else  than  another  way  of  expressing  the 
unresolvable  multiple  relation  of  an  object  to  events. 

A  complete  time-system  is  formed  by  any  one  family 
of  parallel  durations.  Two  durations  are  parallel  if 
either  (i)  one  includes  the  other,  or  (ii)  they  overlap  so 
as  to  include  a  third  duration  common  to  both,  or 
(iii)  are  entirely  separate.  The  excluded  case  is  that  of 
two  durations  overlapping  so  as  to  include  in  common 
an  aggregate  of  finite  events  but  including  in  common 
no  other  complete  duration.  The  recognition  of  the 
fact  of  an  indefinite  number  of  families  of  parallel 
durations  is  what  differentiates  the  concept  of  nature 
here  put  forward  from  the  older  orthodox  concept  of 


IX]      THE  ULTIMATE  PHYSICAL  CONCEPTS     191 

the  essentially  unique  time-systems.  Its  divergence  from 
Einstein's  concept  of  nature  will  be  briefly  indicated  later. 

The  instantaneous  spaces  of  a  given  time-system  are 
the  ideal  (non-existent)  durations  of  zero  temporal 
thickness  indicated  by  routes  of  approximation  along 
series  formed  by  durations  of  the  associated  family. 
Each  such  instantaneous  space  represents  the  ideal  of 
nature  at  an  instant  and  is  also  a  moment  of  time.  Each 
time-system  thus  possesses  an  aggregate  of  moments 
belonging  to  it  alone.  Each  event-particle  lies  in  one 
and  only  one  moment  of  a  given  time-system.  An  event- 
particle  has  three  characters^ :  (i)  its  extrinsic  character 
which  is  its  character  as  a  definite  route  of  convergence 
among  events,  (ii)  its  intrinsic  character  which  is  the 
peculiar  quality  of  nature  in  its  neighbourhood,  namely, 
the  character  of  the  physical  field  in  the  neighbourhood, 
and  (iii)  its  position. 

The  position  of  an  event-particle  arises  from  the 
aggregate  of  moments  (no  two  of  the  same  family)  in 
which  it  lies.  We  fix  our  attention  on  one  of  these 
moments  which  is  approximated  to  by  the  short  dura- 
tion of  our  immediate  experience,  and  we  express 
position  as  the  position  in  this  moment.  But  the  event- 
particle  receives  its  position  in  moment  M  in  virtue  of 
the  whole  aggregate  of  other  moments  M\  M" ,  etc., 
in  which  it  also  lies.  The  differentiation  of  M  into  a 
geometry  of  event-particles  (instantaneous  points)  ex- 
presses the  diflferentiation  of  M  by  its  intersections  with 
moments  of  alien  time-systems.  In  this  way  planes  and 
straight  lines  and  event-particles  themselves  find  their 
being.  Also  the  parallelism  of  planes  and  straight  lines 
arises  from  the  parallelism  of  the  moments  of  one  and 
^  Of.  pp.  82  et  seq. 


192  THE  CONCEPT  OF  NATURE  [ch. 

the  same  time-system  intersecting  M,  Similarly  the 
order  of  parallel  planes  and  of  event-particles  on  straight 
lines  arises  from  the  time-order  of  these  intersecting 
moments.  The  explanation  is  not  given  here^.  It  is 
sufficient  now  merely  to  mention  the  sources  from  which 
the  whole  of  geometry  receives  its  physical  explanation. 

The  correlation  of  the  various  momentary  spaces  of 
one  time-system  is  achieved  by  the  relation  of  cogre- 
dience.  Evidently  motion  in  an  instantaneous  space  is 
unmeaning.  Motion  expresses  a  comparison  between 
position  in  one  instantaneous  space  with  positions  in 
other  instantaneous  spaces  of  the  same  time-system. 
Cogredience  yields  the  simplest  outcome  of  such  com- 
parison, namely,  rest. 

Motion  and  rest  are  immediately  observed  facts. 
They  are  relative  in  the  sense  that  they  depend  on  the 
time-system  which  is  fundamental  for  the  observation. 
A  string  of  event-particles  whose  successive  occupation 
means  rest  in  the  given  time-system  forms  a  timeless 
point  in  the  timeless  space  of  that  time-system.  In  this 
way  each  time-system  possesses  its  own  permanent 
timeless  space  peculiar  to  it  alone,  and  each  such  space 
is  composed  of  timeless  points  which  belong  to  that 
time-system  and  to  no  other.  The  paradoxes  of  rela- 
tivity arise  from  neglecting  the  fact  that  different  as- 
sumptions as  to  rest  involve  the  expression  of  the  facts 
of  physical  science  in  terms  of  radically  different  spaces 
and  times,  in  which  points  and  moments  have  different 
meanings. 

The  source  of  order  has  already  been  indicated  and 
that  of  congruence  is  now  found.  It  depends  on  motion. 

1  Of.  Principles  of  Natural  Knowledge^  and  previous  chapters 
of  the  present  work. 


IX]      THE  ULTIMATE  PHYSICAL  CONCEPTS     193 

From  cogredience,  perpendicularity  arises;  and  from 
perpendicularity  in  conjunction  with  the  reciprocal 
symmetry  between  the  relations  of  any  two  time-systems 
congruence  both  in  time  and  space  is  completely  defined 
(cf.  loc,  cit.). 

The  resulting  formulae  are  those  for  the  electro- 
magnetic theory  of  relativity,  or,  as  it  is  now  termed,  the 
restricted  theory.  But  there  is  this  vital  difference:  the 
critical  velocity  c  which  occurs  in  these  formulae  has 
now  no  connexion  whatever  with  light  or  with  any 
other  fact  of  the  physical  field  (in  distinction  from  the 
extensional  structure  of  events).  It  simply  marks  the 
fact  that  our  congruence  determination  embraces  both 
times  and  spaces  in  one  universal  system,  and  therefore 
if  two  arbitrary  units  are  chosen,  one  for  all  spaces  and 
one  for  all  times,  their  ratio  will  be  a  velocity  which  is  a 
fundamental  property  of  nature  expressing  the  fact  that 
times  and  spaces  are  really  comparable. 

The  physical  properties  of  nature  are  expressed  in 
terms  of  material  objects  (electrons,  etc.).  The  physical 
character  of  an  event  arises  from  the  fact  that  it  belongs 
to  the  field  of  the  whole  complex  of  such  objects.  From 
another  point  of  view  we  can  say  that  these  objects  are 
nothing  else  than  our  way  of  expressing  the  mutual 
correlation  of  the  physical  characters  of  events. 

The  spatio-temporal  measurableness  of  nature  arises 
from  (i)  the  relation  of  extension  between  events,  and 
(ii)  the  stratified  character  of  nature  arising  from  each  of 
the  alternative  time-systems,  and  (iii)  rest  and  motion, 
as  exhibited  in  the  relations  of  finite  events  to  time- 
systems.  None  of  these  sources  of  measurement  depend 
on  the  physical  characters  of  finite  events  as  exhibited 
by  the  situated  objects.  They  are  completely  signified 

W.  N.  13 


194  THE  CONCEPT  OF  NATURE  [ch. 

for  events  whose  physical  characters  are  unknown.  Thus 
the  spatio-temporal  measurements  are  independent  of 
the  objectival  physical  characters.  Furthermore  the 
character  of  our  knowledge  of  a  whole  duration,  which 
is  essentially  derived  from  the  significance  of  the  part 
within  the  immediate  field  of  discrimination,  constructs 
it  for  us  as  a  uniform  whole  independent,  so  far  as  its 
extension  is  concerned,  of  the  unobserved  characters 
of  remote  events.  Namely,  there  is  a  definite  whole  of 
nature,  simultaneously  now  present,  whatever  may  be 
the  character  of  its  remote  events.  This  consideration 
reinforces  the  previous  conclusion.  This  conclusion 
leads  to  the  assertion  of  the  essential  uniformity  of  the 
momentary  spaces  of  the  various  time-systems,  and 
thence  to  the  uniformity  of  the  timeless  spaces  of  which 
there  is  one  to  each  time-system. 

The  analysis  of  the  general  character  of  observed 
nature  set  forth  above  aflFords  explanations  of  various 
fundamental  observational  facts:  (a)  It  explains  the 
differentiation  of  the  one  quality  of  extension  into  time 
and  space.  (^S)  It  gives  a  meaning  to  the  observed  facts 
of  geometrical  and  temporal  position,  of  geometrical 
and  temporal  order,  and  of  geometrical  straightness  and 
planeness.  (y)  It  selects  one  definite  system  of  congruence 
embracing  both  space  and  time,  and  thus  explains  the 
concordance  as  to  measurement  which  is  in  practice 
attained.  (S)  It  explains  (consistently  with  the  theory  of 
relativity)  the  observed  phenomena  of  rotation,  e.g. 
Foucault's  pendulum,  the  equatorial  bulge  of  the  earth, 
the  fixed  senses  of  rotation  of  cyclones  and  anticyclones, 
and  the  gyro-compass.  It  does  this  by  its  admission  of 
definite  stratifications  of  nature  which  are  disclosed  by 
the  very  character  of  our  knowledge  of  it.   (c)  Its  ex- 


IX]      THE  ULTIMATE  PHYSICAL  CONCEPTS     195 

planations  of  motion  are  more  fundamental  than  those 
expressed  in  (8) ;  for  it  explains  what  is  meant  by  motion 
itself.  The  observed  motion  of  an  extended  object  is 
the  relation  of  its  various  situations  to  the  stratification 
of  nature  expressed  by  the  time-system  fundamental  to 
the  observation.  This  motion  expresses  a  real  relation 
of  the  object  to  the  rest  of  nature.  The  quantitative 
expression  of  this  relation  will  vary  according  to  the 
time-system  selected  for  its  expression. 

This  theory  accords  no  peculiar  character  to  light 
beyond  that  accorded  to  other  physical  phenomena  such 
as  sound.  There  is  no  ground  for  such  a  differentiation. 
Some  objects  we  know  by  sight  only,  and  other  objects 
we  know  by  sound  only,  and  other  objects  we  observe 
neither  by  light  nor  by  sound  but  by  touch  or  smell  or 
otherwise.  The  velocity  of  light  varies  according  to  its 
medium  and  so  does  that  of  sound.  Light  moves  in 
curved  paths  under  certain  conditions  and  so  does 
sound.  Both  light  and  sound  are  waves  of  disturbance 
in  the  physical  characters  of  events ;  and  (as  has  been 
stated  above,  p.  188)  the  actual  course  of  the  light 
is  of  no  more  importance  for  perception  than  is  the 
actual  course  of  the  sound.  To  base  the  whole  philo- 
sophy of  nature  upon  light  is  a  baseless  assumption. 
The  Michelson-Morley  and  analogous  experiments 
show  that  within  the  limits  of  our  inexactitude  of 
observation  the  velocity  of  light  is  an  approximation  to 
the  critical  velocity  ^ c^  which  expresses  the  relation 
between  our  space  and  time  units.  It  is  provable  that 
the  assumption  as  to  light  by  which  these  experiments 
and  the  influence  of  the  gravitational  field  on  the  light- 
rays  are  explained  is  deducible  as  an  approximation 
from  the  equations  of  the  electromagnetic  field.  This 


196  THE  CONCEPT  OF  NATURE  [ch. 

completely  disposes  of  any  necessity  for  differentiating 
light  from  other  physical  phenomena  as  possessing 
any  peculiar  fundamental  character. 

It  is  to  be  observed  that  the  measurement  of  extended 
nature  by  means  of  extended  objects  is  meaningless 
apart  from  some  observed  fact  of  simultaneity  inherent 
in  nature  and  not  merely  a  play  of  thought.  Otherwise 
there  is  no  meaning  to  the  concept  of  one  presentation 
of  your  extended  measuring  rod  AB.  Why  not  AB' 
where  B'  is  the  end  B  five  minutes  later  ?  Measurement 
presupposes  for  its  possibility  nature  as  a  simultaneity, 
and  an  observed  object  present  then  and  present  now. 
In  other  words,  measurement  of  extended  nature  re- 
quires some  inherent  character  in  nature  affording  a 
rule  of  presentation  of  events.  Furthermore  congruence 
cannot  be  defined  by  the  permanence  of  the  measuring 
rod.  The  permanence  is  itself  meaningless  apart  from 
some  immediate  judgment  of  self-congruence.  Other- 
wise how  is  an  elastic  string  differentiated  from  a  rigid 
measuring  rod?  Each  remains  the  same  self-identical 
object.  Why  is  one  a  possible  measuring  rod  and  the 
other  not  so  ?  The  meaning  of  congruence  lies  beyond 
the  self-identity  of  the  object.  In  other  words  measure- 
ment presupposes  the  measurable,  and  the  theory  of  the 
measurable  is  the  theory  of  congruence. 

Furthermore  the  admission  of  stratifications  of  nature 
bears  on  the  formulation  of  the  laws  of  nature.  It  has 
been  laid  down  that  these  laws  are  to  be  expressed  in 
differential  equations  which,  as  expressed  in  any  general 
system  of  measurement,  should  bear  no  reference  to 
any  other  particular  measure-system.  This  requirement 
is  purely  arbitrary.  For  a  measure-system  measures 
something  inherent  in  nature;   otherwise   it  has   no 


IX]       THE  ULTIMATE  PHYSICAL  CONCEPTS      197 

connexion  with  nature  at  all.  And  that  something  which 
is  measured  by  a  particular  measure-system  may  have  a 
special  relation  to  the  phenomenon  whose  law  is  being 
formulated.  For  example  the  gravitational  field  due  to 
a  material  object  at  rest  in  a  certain  time-system  may 
be  expected  to  exhibit  in  its  formulation  particular 
reference  to  spatial  and  temporal  quantities  of  that 
time-system.  The  field  can  of  course  be  expressed  in 
any  measure-systems,  but  the  particular  reference  will 
remain  as  the  simple  physical  explanation. 

NOTE:  ON  THE  GREEK  CONCEPT  OF  A  POINT 

The  preceding  pages  had  been  passed  for  press  before  I  had 
the  pleasure  of  seeing  Sir  T.  L.  Heath's  Euclid  in  Greek^. 
In  the  original  Euclid's  first  definition  is 

a-rjfjLelov  iaTCVy  ov  fiipof;  ovdev. 
I  have  quoted  it  on  p.  86  in  the  expanded  form  taught  to  me 
in  childhood,  *  without  parts  and  without  magnitude.'  I  should 
have  consulted  Heath's  English  edition — a  classic  from  the 
moment  of  its  issue — before  committing  myself  to  a  statement 
about  Euclid.  This  is  however  a  trivial  correction  not  affecting 
sense  and  not  worth  a  note.  I  wish  here  to  draw  attention  to 
Heath's  own  note  to  this  definition  in  his  Euclid  in  Greek.  He 
summarises  Greek  thought  on  the  nature  of  a  point,  from  the 
Pythagoreans,  through  Plato  and  Aristotle,  to  Euclid.  My 
analysis  of  the  requisite  character  of  a  point  on  pp.  89  and 
90  is  in  complete  agreement  with  the  outcome  of  the  Greek 
discussion. 

NOTE:  ON  SIGNIFICANCE  AND  INFINITE  EVENTS 

The  theory  of  significance  has  been  expanded  and  made  more 
definite  in  the  present  volume.  It  had  already  been  introduced 
in  the  Principles  of  Natural  Knowledge  (cf.  subarticles  3-3  to 
3-8  and  i6-i,  16-2, 19-4,  and  articles  20, 21).  In  reading  over  the 
proofs  of  the  present  volume,  I  come  to  the  conclusion  that  in  the 

1  Camb.  Univ.  Press,  1920. 

13—3 


198  THE  CONCEPT  OF  NATURE  [ch.ix 

light  of  this  development  my  limitation  of  infinite  events  to  dura- 
tions is  untenable.  This  limitation  is  stated  in  article  33  of  the 
Principles  and  at  the  beginning  of  Chapter  IV  (p.  74)  of  this  book. 
There  is  not  only  a  significance  of  the  discerned  events  embracing 
the  whole  present  duration,  but  there  is  a  significance  of  a  cogre- 
dient  event  involving  its  extension  through  a  whole  time-system 
backwards  and  forwards.  In  other  words  the  essential '  beyond' 
in  nature  is  a  definite  beyond  in  time  as  well  as  in  space  [cf. 
pp.  53, 194].  This  follows  from  my  whole  thesis  as  to  the  assimila- 
tion of  time  and  space  and  their  origin  in  extension.  It  also  has 
the  same  basis  in  the  analysis  of  the  character  of  our  knowledge 
of  nature.  It  follows  from  this  admission  that  it  is  possible  to 
define  point-tracks  [i.e.  the  points  of  timeless  spaces]  as  abstrac- 
tive elements.  This  is  a  great  improvement  as  restoring  the 
balance  between  moments  and  points.  I  still  hold  however  to  the 
statement  in  subarticle  35-4  of  the  Principles  that  the  intersection 
of  a  pair  of  non-parallel  durations  does  not  present  itself  to  us  as 
one  event.  This  correction  does  not  affect  any  of  the  subsequent 
reasoning  in  the  two  books. 

I  may  take  this  opportunity  of  pointing  out  that  the '  stationary 
events'  of  article  57  of  the  Principles  are  merely  cogredient 
events  got  at  from  an  abstract  mathematical  point  of  view. 


INDEX 


In  the  case  of  terms  of  frequent  occurrence,  only  those  occurrences  are 
indexed  which  are  of  peculiar  importance  for  the  elucidation  of  meaning. 


A  [or  an],  ii 

Abraham,  105 

Absolute   position,    105,    106,    114, 

188 
Abstraction,  33,  37,  168,  171,  173; 

extensive,  65,  79,  85 
Abstractive    element,    84;    set,    61, 

79 
Action  at  a  distance,  159,  190 
Action  by  transmission,  159,  190 
Active  conditions,  158 
Activity,  field  of,  170,  181 
Adjunction,  loi 
Aggregate,  23 
Alexander,  Prof.,  viii 
Alexandria,  71 
Alfred  the  Great,  137 
Anticipation,  69 
Anti-prime,  88 
Apparent  nature,  31,  39 
Area,  99;  momental,  103;  vagrant, 

103 
Aristotelian  logic,  150 
Aristotle,  16,  17,  18,  24,  197 
Associate-potential,  183 
Atom,  17 

Attribute,  21,  26,  150 
Awareness,  3 
Axiom,  36,  121 
Axioms  of  congruence,  128  at  seqq. 

Bacon,  Francis,  78 
Behaviouristic,  185 
Bergson,  54 
Berkeley,  28 
Between,  64 
Beyond,  186,  198 
Bifurcation,  vi,  30,  185,  187 
Boundary,  100;  moment,  63;  par- 
ticle, 100 
Broad,  C.  D.,  viii 

Calculation,  formula  of,  45,  158 
Cambridge,  97 
Causal  nature,  31,  39 
Causation,  31,  146 
Centrifugal  force,  138 
Change,  uniformity  of,  140 


Character,  extrinsic,  82,  89,  90,  113, 
191;  intrinsic,  80,  82,  90,  113,  191 

Charge,  160 

Closure  of  nature,  4 

Coefficient  of  drag,  133 

Coefficients  of  impetus,  183 

Cogredience,  no,  188 

Coherence,  29 

Comparison,  124,  125,  143,  189 

Complex,  13 

Conceptual  nature,  45;  space,  96 

Concrete  facts,  167,  171,  189 

Conditioning  events,  152 

Conditions,  active,  158 

Congruence,  65,  96, 118, 120,  127, 196 

Continuity,  157;  Dedekindian,  102; 
of  events,  76;  of  nature,  59,  76 

Convention,  121 

Convergence,  62,  79;  law  of,  82 

Conveyance,  154,  155 

Co-present,  177 

Covering,  83 

Creative  advance,  178 

Critical  velocity,  193,  195 

Curvature  of  space- time,  182 

Cyclone,  194 

Dedekindian  continuity,  102 
Definite,  53,  194,  198 
Delusions,  31,  38 
Delusive  perceptual  object,  153 
Demarcation  of  events,  144 
Demonstrative  phrase,  6 
Descriptive  phrase,  6,  10 
Differential  equations,  196 
Discrimination,  14,  50,  144 
Diversification  of  nature,  15 
Duddington,  Mrs,  47 
Duration,  37.  53.  55.  186 
Durations,  families  of,  59,  73,  190 
Dynamical  axes,  138 

Einstein,   vii,    102,    131,    164,    165, 

181,  182,  183,  184,  191 
Electromagnetic  field,  179 
Electron,  30,  146,  158,  171 
Element,  17;  abstractive,  84 
Elliptical  phraseology,  7 


200 


INDEX 


Empty  space,  145 

Entity,  5,  13 

Equal  in  abstractive  force,  83 

Error,  68 

Ether,  18,  78,  160;  material,  78; 
of  events,  78 

Euclid,  85,  94,  197 

Euler,  140 

Event,  15,  52,  75,  165;  percipient, 
107,  152,  186 

Event-particle,  86,  93,  94,  172,  191 

Events,  conditioning,  152;  con- 
tinuity of,  76;  demarcation  of, 
144;  ether  of,  78;  infinite,  197, 
198;  limited,  74;  passage  of,  34; 
signified,  52;  stationary,  198; 
stream  of,  167;  structure  of,  52, 
166 

Exclusion,  186 

Explanation,  97,  141 

Extended  nature,  196 

Extension,  22,  58,  75,  185 

Extensive  abstraction,  65,  79,  85 

Extrinsic  character,  82,  89,  90,  113, 
191;  properties,  62 

Fact,  12,  13 

Factors,  12,  13,  15 

Facts,  concrete,  167,  171 

Family  of  durations,  59,  63,  73;  of 

moments,  63 
Faraday,  146 
Field,  gravitational,  197;  of  activity, 

170,  181;  physical,  190 
Finite  truths,  12 
Fitzgerald,  133 

Formula  of  calculation,  45,  158 
Foucault,  138,  194 
Four-dimensional  manifold,  86 
Fresnel,  133 
Future,  the,  72,  177 

Galileo,  139 

Geometrical  order,  194 

Geometry,  36;  metrical,  129 

Gravitation,  179  et  seqq. 

Gravitational  field,  197 

Greek  philosophy,  16;  thought,  197 

Gyro-compass,  194 

Heath,  Sir  T.  L.,  197 
Here,  107 

Idealists,  70 

Immediacy,  52;  of  perception,  72 

Impetus,   181,   182;    coefficients  of, 

183;  integral,  183 
Inclusion,  186 
Individuality,  13 


Infinite  events,  197,  198 

Inge,  Dr,  48 

Ingredient,  14 

Ingression,  144,  145,  148,  152 

Inherence,  8^ 

Inside,  106 

Instant,  33,  35,  57 

Instantaneous  plane,  91 ;  present,  72 ; 

spaces,  86,  90,  177 
Instantaneousness,  56,  57 
Intersection,  locus  of,  90 
Intrinsic  character,  80,  82,  90,  113, 

191;  properties,  62 
Ionian  thinkers,  19 
Irrelevance,  infinitude  of,  12 
Irrevocableness,  35,  37 
It,  8 

Julius  Caesar,  36 
Junction,  76,  loi 

Kinetic  energy,  105;  symmetry,  129 
Knowledge,  28,  32 

Lagrange,  140 

Larmor,  131 

Law  of  convergence,  82 

Laws  of  motion,  137,  139;  of  nature, 

196 
Leibnizian  monadology,  150 
Level,  91,  92 
Light,  195;  ray  of,  188;  velocity  of, 

131 
Limit,  57 

Limited  events,  74 
Location,  160,  161 
Locke,  27 

Locus,  102;  of  intersection,  90 
London,  97 

Lorentz,  H.  A.,  131,  133 
Lossky,  47 

Manifold,     four-dimensional,      86; 

space-time,  173 
Material  ether,  78;  object,  169 
Materialism,  43,  70 
Matrix,  116 

Matter,  16,  17,  19,  20,  26 
Maxwell,  131,  133 
Measurableness,  196;  of  nature,  193 
Measurement,  96,  120,  174,  196;  of 

time,  65,  140 
Measure-system,  196 
Memory,  68 
Metaphysics,  28,  32 
Metrical  geometry,  129 
Michelson-Morley,  195 
Milton,  35 
Mind,  27,  28 


INDEX 


201 


Minkowski,  viii,  131 

Molecule,  32,  171 

Moment,  57,  60,  88 

Momental  area,  103;  route,  103 

Momentum,  105 

Motion,  105,  114,  117,  127,  188,  192 

Multiplicity,  22 

Natural  philosophy,  29,  30 
Natural  science,  philosophy  of,  46 
Nature,  3;  apparent,  31,  39;  causal, 

31,  39;  conceptual,  45;  continuity 

of,  59,  76;  discrimination  of,  144; 

extended,     196;     laws    of,     196; 

passage  of,  54;  stratification  of, 

194,  196;  system  of,  146 
Newton,  27,  136,  139,  140 

Object,  77,  125,  143,  169,  189; 
delusive  perceptual,  155;  material, 
169;  perceptual,  153;  physical, 
155.  ''^57>  scientific,  158,  169;  uni- 
form, 162 

Occupation,  22,  34,  36,  100,  loi 

Order,  source  of,  192;  spatial,  95, 
194;  temporal,  64,  95,  194 

Organisation  of  thought,  79 

Outside,  63,  100 

Paradox,  192 

Parallel,  63,  127;  durations,  190    - 

Parallelism,  95,  191 

Parallelogram,  127 

Paris,  87,  138 

Parliament,  120 

Part,  14,  15,  58 

Passage  of  events,  34;  of  nature,  54 

Past,  the,  72,  177 

Perception,  3 

Perceptual  objects,  149,  153 

Percipience,  28 

Percipient  event,  107,  152,  186,  187 

Period  of  time,  51 

Permanence,  144 

Perpendicularity,  117,  127,  193 

Philosophy,  i ;   natural,   29,   30 ;   of 

natural  science,  46 ;  of  the  sciences, 

2 
Physical  field,  190;  object,  155,  156, 

157 
Physics,  speculative,  30 
Place,  51 

Plane,  191;  instantaneous,  91 
Plato,  16,  17,  18,  24,  197 
Poincare,  121,  122,  123 
Point,  35,  89,^91,  114,  173,  176 
Point-flash,  172,  173 
Point  of  space,  85 
Point,  timeless,  192 


Point- track,  113,  198 

Pompey,  36 

Position,  89,  90,  92,  93,  99,  113,  191 J 
absolute,  105,  106,  114,  188 

Potential,  183;  associate-,  183 

Predicate,  18 

Predication,  18 

Present,  the,  69,  72,  177;  instan- 
taneous, 72;  observational,  186 

Primary  qualities,  27 

Prime,  88 

Process,  53,  54;  of  nature,  54 

Psychic  additions,  29,  187 

Punct,  92,  93,  94 

Pythagoreans,  197 

Quality,  27 
Quantum  of  time,  162 
Quantum  theory,  162 

Ray  of  light,  188 

Reality,  30;  of  durations,  55,  187 

Recognition,  124,  143,  189 

Rect,  91,  92 

Recurrence,  35 

Relative  motion,  117;  velocity,  130 

Relativity,  169;    restricted    theory 

of,  193 
Rest,  105,  114,  188,  192 
Rotation,  138,  194 
Route,  99;  momental,  103;  straight, 

103 
Russell,  Bertrand,  11,  122,  123 

Schelling,  47 

Science,  2;  metaphysical,  32 
Scientific  objects,  149,  158,  169 
Secondary  qualities,  27 
Self-congruence,  196 
Self-containedness  of  nature,  4 
Sense-awareness,  3,  67 
Sense-object,  149,  170 
Sense-perception,  3,  14 
Sense-recognition,  143,  189 
Series,  temporal,  66,  70,  85,  178 
Set,  abstractive,  61,  79 
Significance,  51,  186,  187,  188,  194, 

197,  198 
Signified  events,  52 
Simplicity,  163,  173 
Simultaneity,  53,  56,  196 
Situation,  15,  78,  147,  148,  152,  160, 

189 
Solid,  99,  loi,  102;  vagrant,  loi 
Sound,  195 
Space,  16,  17.  31.33,  79;  empty,  145; 

timeless,  86,  106,  114;  uniformity 

of,  194 
Spaces,  instantaneous,  86,  90 


202 


INDEX 


Space-system,  179 
Space- time  manifold,  173 
Spatial-order,  95 
Spatio-temporal  structure,  173 
Speculative  demonstration,  6 
Speculative  physics,  30 
Standpoint  for  perception,  107,  188 
Station,  103,  104,  113 
Stationary  events,  198 
Straight  line,  91,  114,  191;    route, 

103 
Stratification  of  nature,    187,    194, 

196 
Stream  of  events,  167 
Structure  of  events,  52,  166 
Structure,  spatio-temporal,  173 
Subject,  18 

Substance,  16,  18,  19,  150 
Substratum,  16,  18,  21 
Symmetry,  118,  126;  kinetic,  129 
System  of  nature,  146 
System,  time-,  192 

Tamer,  Edward,  v,  i 

Temporal  order,  64,  95,  194 

Temporal  series,  66,  70,  85 

Tensor,  182 

Terminus,  4 

The,  II 

Theory,  quantum,  162 

There,  no,  189 

This,  II 

Thought,  3,  14 


Timaeus,  the,  17,  20,  24 

Time,     16,     17,     31,     33,     49.     79; 

measurement  of,  140;  quantum  of, 

162;  transcendence  of,  39 
Time-series,  178,  also  cf.  Temporal 

series 
Time-system,   see  Time-series,  also 

91,  97,  104,  179,  192 
Timeless  point,  192;  space,  86,  106, 

114.  177 
Totality,  89 

Transcendence  of  time,  39 
Transmission,  26,  28;  action  by,  159, 

190 
Tubes  of  force,  146 

Unexhaustiveness,  50 
Uniform  object,  162 
Uniformity  of  change,  140;  of  space, 
194 

Vagrant  area,  103 ;  solid,  loi 

Veblen  and  Young,  36 

Velocity,  critical,  193,  195;  of  liglit, 

131,  195;  relative,  130 
Volume,  92,  10 1 

When,  107 
Where,  107 
Whole,  58 
Within,  63 

Young,  Veblen  and,  36 


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